One of the thoughts as to why humans cannot grow post fusion is due to the belief that chondrocytes cannot grow organically.  There are lots of stem cells present in the 
bone marrow, as can be seen by the large amount of red dots present in the bone marrow such as in the link shown above.  If you look at these diagrams of 
epiphyseal distraction, you can see that everything else ossifies aside from the hyaline cartilage growth plate line(there is ossification within the hyaline cartilage as a result of microfracture; growth plate injuries often create a bony bridge in the fracture site; even in the very gradual epiphyseal distraction method there was still some ossification).
The goal of lateral synovial joint loading is to increase interstitial fluid flow by using methods such as the table clamp to send mesenchymal stem cells to the hyaline cartilage growth plate line where they will undergo a chondrogenic lineage.  If you look at the rat's under LSJL slide(right click and click on view image to see it in it's entirety) you can see stem cells being captured and taken into the hyaline cartilage growth plate line in slide B.  Can chondrogenesis be induced organically despite growth plate fusion?
Hydrostatic pressure enhances chondrogenic differentiation of human bone marrow stromal cells in osteochondrogenic medium. 
Interstitial fluid flow such as that created by using the table clamp or pressing on the epiphysis of the bone with the dumbell increases hydrostatic pressure. 
"This study demonstrated the chondrogenic effect of hydrostatic pressure  on human bone marrow stromal cells[LSJL encourages chondrogenic differentiation of stromal cells, stem cells are a subset of stromal cells] (MSCs) cultured in a mixed medium  containing osteogenic and chondrogenic factors. MSCs seeded in type I  collagen sponges were exposed to 1 MPa of intermittent hydrostatic  pressure at a frequency of 1 Hz for 4 h per day for 10 days[1 Hz means load for a duration of 1 second, 1 MPa is the type of pressure used in steam locomotives, standard atmospheric pressure is 0.1 MPa at sea level], or remained  in identical culture conditions but without exposure to pressure. we compared the proteoglycan content of loaded and control  cell/scaffold constructs with Alcian blue staining. We evaluate the change in mRNA expression of selected  genes associated with chondrogenic and osteogenic differentiation  (aggrecan, type I collagen, type II collagen, Runx2 (Cbfa-1), Sox9, and  TGF-beta1)[Most of these genes are associated with chondrogenic differentiation with the exception of Runx2]. With the hydrostatic pressure loading regime, proteoglycan  staining increased markedly. the mRNA expression of  chondrogenic genes such as aggrecan, type II collagen, and Sox9  increased significantly. We also saw a significant increase in the mRNA  expression of type I collagen, but no change in the expression of Runx2  or TGF-beta1 mRNA. This study demonstrated that hydrostatic pressure  enhanced differentiation of MSCs in the presence of multipotent  differentiation factors in vitro, and suggests the critical role that  this loading regime may play during cartilage development and  regeneration in vivo." 
"MSCs can differentiate along the chondrogenic lineage in three-dimensional culture conditions in the presence of soluble regulatory factors such as members of the TGF-β family. Other chondrogenic influences on the differentiation of mesenchymal cells are certain types of mechanical loading. Hydrostatic pressure and compressive loading[lateral joint loading results in compressive forces against the chondrocytes as well as well] increased cartilage matrix accumulation in cultured MSCs and in embryonic limb bud cells in vitro."
"Without the addition of TGF-β, the effects of mechanical stimuli are unclear;
 in some studies                mechanical stimuli alone was sufficient to induce skeletal progenitor cells to adopt the cartilage phenotype"
"Loaded                   scaffolds were exposed to 1 MPa of pressure at a  loading frequency of 1 Hz for 4 h per day, as this loading regime had  previously                   been found to be effective in inducing chondrogenesis."
"The duration of the experiment was 10 days, as the results of a pilot study indicated that chondrogenic matrix accumulation                   could be visualized at this timepoint."
It's unclear whether the stem cells remained in an 
hypoxic environment. 
"the hydrostatic pressure protocol increased the mRNA expression of both collagen I and II"
This mixture could lead to fibrocartilage rather than hyaline cartilage the authors speculate. 
This was the medium used in the study: "1.0 mg/mL insulin, 0.55 mg/mL transferrin, 0.5 
μg/mL sodium selenite, 50 mg/mL bovine serum albumin, 470 
μg/mL linoleic acid), 10 nM dexamethasone, 50 
μg/mL 
l-ascorbic acid, 1 mM sodium pyruvate, 40 
μg/mL 
l-proline, 0.584 g/L 
l-glutamine, and 100 IU each penicillin and streptomycin."
Most of this aside for example the dexamethasone is available in the human body. 
Previously, we found that periosteal loading increased expression of TGF-Beta whereas dynamic loading of chondrocytes increased expression of aggrecan and type II Collagen.  Dynamic loading of chondrocytes did not increase expression of Sox9 which is very important in endochondral ossification.  In the LSJL, studies Sox9 was not upregulated, however, the scientists only studied gene expression by bone and not by cartilage.  This study found that TGF Beta1 was not upregulated in contrast to LSJL which found that TGF Beta 1 was upregulated.  A possible explanation for this is that the collagen sponges contained no periosteum.   
Bone contains a lot of Type I collagen which was the medium used for the stem cells in the study.  So that part of the study is easy to recreate.  Hydrostatic pressure is pretty synonymous with interstitial fluid flow so that part of the study can be recreated by LSJL.  One thing you'll notice is that the stem cells were not in the hyaline cartilage growth plate line.  This means that chondrogenesis can occur organically even without an open growth plate.
Effects of hydrostatic pressure and transforming  growth factor-beta 3 on adult human mesenchymal stem cell chondrogenesis  in vitro.
"[What are] the effects of intermittent hydrostatic pressure  (IHP) and transforming growth factor-beta 3 on chondrogenesis of adult  human mesenchymal stem cells (hMSCs) in vitro? Chondrogenic gene  expression was determined by quantifying mRNA signal levels for SOX9, a  transcription factor critical for cartilage development and the  cartilage matrix proteins, aggrecan and type II collagen. Extracellular  matrix production was determined by weight and histology.
 IHP was  applied to hMSCs in pellet culture at a level of 10 MPa[the amount of pressure used by a pressure washer] and a frequency  of 1 Hz for 4 h per day for periods of 3, 7, and 14 days. hMSCs  responded to addition of TGF-beta 3 (10 ng/mL) with a greater than  10-fold increase (p < 0.01) in mRNA levels for each, SOX9, type II  collagen, and aggrecan during a 14-day culture period. Applying IHP in  the presence of TGF-beta 3 further increased the mRNA levels for these  proteins by 1.9-, 3.3-, and 1.6-fold, respectively, by day 14.  
Chondrogenic mRNA levels were increased with just exposure to IHP.  Extracellular matrix deposition of type II collagen and aggrecan  increased in the pellets as a function of treatment conditions and time  of culture. This study demonstrated adjunctive effects of IHP on  TGF-beta 3-induced chondrogenesis."
 
"Normal hMSCs (positive for CD105, CD166, CD29, and CD44 and negative for CD14, CD34, and CD45) from normal human bone marrow"
"Hip joint contact pressures up to 18 MPa exist during some activities, such as rising from a chair[but note this pressure is not applied within the epiphysis of the bone]"
"The effect of IHP on SOX9 expression may involve changes in cytoskeletal organization, G-protein activation, and transcription factor translocation into the nucleus."
Here's an example of what a stem cell looks like with intermittent hydrostatic pressure applied:
The HE and Saf-O refers to a form of staining.  TGF-Beta3 +IHP is better but IHP is good enough to induce chondrogenic differentiation.  "IHP applied with and without addition of TGF-Beta3 also increased gene expression for all three chondrogenic proteins[Aggrecan, Sox9, Type II Collagen]."
I can't really think of a good way to measure pressure for LSJL as all the pressure gauges are for tires and water level.
Stem cells are sensitive to mechanotransduction which makes their mechanosensitivity important.  Hydrostatic Pressure induces dynamic compression as it's the flow of the fluid that makes the compression dynamic.
Dose- and time-dependent effects of cyclic hydrostatic pressure on transforming growth factor-beta3-induced chondrogenesis by adult human mesenchymal stem cells in vitro.
"MSCs were exposed to 0.1, 1, and 10 MPa of IHP at a frequency of 1 Hz for 4 h/day for 3, 7, and 14 days in the presence of transforming growth factor (TGF-beta3). Chondrogenesis was characterized by gene expression, macromolecule production, and extracellular matrix deposition. Exposure of hMSCs to 0.1 MPa of IHP increased SOX9 and aggrecan mRNA expression by 2.2- and 5.6-fold, respectively, whereas type II collagen mRNA expression responded maximally at 10 MPa. Production of sulfated glycosaminoglycan responded to IHP of 1 MPa and 10 MPa, whereas collagen levels increased only at 10 MPa. Morphologically, matrix condensation occurred with increased IHP, concomitant with collagen expression. Different levels of IHP differentially modulate hMSC chondrogenesis in the presence of TGF-beta3."
"hydrostatic pressure (50 MPa) [induces] heat shock proteins[HSP70]."  5MPa to cartilage increases TGFB3 levels.
"[Stem] Cells were positive for CD105, CD166, CD29, and CD44 and negative for CD14, CD34, and CD45."
Dynamic compression regulates the expression and  synthesis of chondrocyte-specific matrix molecules in bone marrow  stromal cells.
"[We] investigate the  mechanotransduction of bovine bone marrow stromal cells (BMSCs) through  the interactions between transforming growth factor beta1 (TGF-beta1),  dexamethasone, and dynamic compressive loading. The
 addition of  TGF-beta1 increased cell viability, extracellular matrix (ECM) gene  expression, matrix synthesis, and sulfated glycosaminoglycan content  over basal construct medium[Stimulating the other bone cells increases TGF-Beta1 which induces all these pro-chondrogenic effects]. The addition of dexamethasone further  enhanced extracellular matrix gene expression and protein synthesis[dexamethasone is not needed].  There was little stimulation of ECM gene expression or matrix synthesis  in any medium group by mechanical loading introduced on day 8. There was significant stimulation of ECM gene expression and  matrix synthesis in chondrogenic media by dynamic loading introduced on  day 16. 
The level of stimulation was also dependent on the medium  supplements, with the samples treated with basal medium being the least  responsive and the samples treated with TGF-beta1 and dexamethasone  being the most responsive at day 16. Collagen I and collagen II  gene expressions were more responsive to dynamic loading than aggrecan  gene expression. Dynamic compression upregulated Smad2/3 phosphorylation  in samples treated with basal and TGF-beta1 media. Interactions between mechanical stimuli and TGF-beta  signaling may be an important mechanotransduction pathway for BMSCs, and  they indicate that 
mechanosensitivity may vary during the process of  chondrogenesis."
TGF-Beta1 affects mechanical sensitivity of bone marrow mesenchymal stem cells.
"TGF-β signals from the cell surface via a transmembrane serine/threonine kinase receptor complex.  
Upon ligand binding, the type II receptor subunit engages and  transphosphorylates a type I receptor subunit (TβRI), which in turn  phosphorylates the receptor-activated Smad proteins (R-Smads) Smad2 and  Smad3[So we want TGF-Beta to be released from the osteoblast cell surface and then engage a type I receptor subunit in a mesenchymal stem cell]. A protein complex with Smad4 forms with the activated R-Smads and  translocates into the nucleus, where the complex interacts with  additional transcription factors, binding to the promoters of responsive  genes and regulating their expression by cooperating with other  activators or repressors.  In addition to the Smad pathway, TGF-β  [activates] signaling pathways, including p38 mitogen-activated protein kinase  (MAPK) and protein kinase C (PKC).  TGF-β signaling [activates] the p38 MAPK pathway  through activation of mitogen-activated protein kinase kinase 1 and  subsequent ERK/ELK signaling. 
G-protein-dependent activation of PKC  results from TGF-β stimulation of growth plate chondrocytes. TGF-β responsiveness 
may require the activation of the R-Smad2/4 complexes[lack of response to LSJL may be a failure of the R-Smad2/4 complex], as well as other signaling pathways"
"dexamethasone induced Sox9 upregulation in the pluripotent mesoblastic C1 line"
TGF-Beta1 plus Dynamic Compression(hydrostatic pressure) = chondrogenic differentiation = height growth
Evidence that hydrostatic pressure can induce differentiation in vitro:
The mechanical environment of bone marrow: a review.
"Bone marrow is a viscous tissue that resides in the confines of bones  and houses pluripotent stem cells. Due to its  confinement by bones, 
the marrow has a unique mechanical environment  which has been shown to be affected from external factors, such as  physiological activity and disuse. 
The mechanical environment of bone  marrow can be defined by determining hydrostatic pressure, fluid flow  induced shear stress, and viscosity. 
The hydrostatic pressure values of  bone marrow reported in the literature vary in the range of 10.7-120  mmHg for mammals[This is the value we are trying to increase with LSJL], which is generally accepted to be around one fourth of  the systemic blood pressure. Viscosity values of bone marrow have been  reported to be between 37.5 and 400 cP for mammals, which is dependent  on the marrow composition and temperature. Marrow's mechanical and  compositional properties have been implicated to be changing during  common bone diseases, aging or disuse. 
In vitro experiments have  demonstrated that the resident mesenchymal stem and progenitor cells in  adult marrow are responsive to hydrostatic pressure[Lateral Loading can affect mesenchymal stem cells], fluid shear or to  local compositional factors such as medium viscosity. Therefore, the  changes in the mechanical and compositional microenvironment of marrow  may affect the fate of resident stem cells in vivo as well, which in  turn may alter the homeostasis of bone."
 
"The close proximity of marrow within medullary cavities                of bones subject the marrow to physiological loads as well"<-Lateral loading can affect the bone marrow.
"When the marrow hematopoietic activity increases, adipose tissue                   undergoes resorption to provide more space, or vice versa."<-If Adipose Tissue is inversly related to bone marrow activity then fat gain may be bad for height growth.
"Bone nutrient vessels enter the marrow cavity to make connections with  marrow                      vessels. Small arteries of marrow also enter the  bone, make a loop and return back to where they originated from"<-So it could be possible for chondrogenic stem cells to travel to where they are needed.
"The fixed femurs of rats 
in vivo [had loads applied] ranging from 0 to 12.25 kg for 1 min. Pressure values [rised] two-fold (12–14 mmHg increase)                   upon loading."12.25 kg is about 25 lbs so 25lbs increases hydrostatic pressure by about 12-144 mmHG, a very useful measurement for performing LSJL.  Note that larger animals like dogs tend to have larger hydrostatic pressure values than mice.
"Contraction of the quadriceps muscles with electrical stimulation [resulted] in a pressure                   increase of 60 mmHg"<-So if you contract your muscles at the same as performing LSJL you can get a larger pressure gain.
"In a tubular bone, the nutrient artery enters the marrow cavity, runs longitudinally in the center, then branches out toward the endosteum of the surrounding bone, leading to specialized vascular structures known as sinuses or sinusoids. Several of these sinuses may then combine to form collecting sinuses which lead to the central sinus or vein. This vein runs longitudinally next to the nutrient artery. Blood in marrow flows from the center toward the bone and then returns back to the center. This structural configuration yields high numbers of vessels and sinuses in the periphery (resulting in a slower flow rate of blood and higher surface area) where most of the exchange occurs. Therefore, hematopoiesis is maximal in the closer proximities to the bone surface leaving the central parts with relatively little hematopoietic activity. Due to this fact, it is possible to observe a transition region between red marrow and fatty marrow radially (red marrow being closer to the endosteal surfaces. Similarly, a longitudinal macroscopic distribution is observed as red marrow in the proximal half and fatty marrow in the distal half of the bones. Bone and marrow are connected by vasculature. Bone nutrient vessels enter the marrow cavity to make connections with marrow vessels. Small arteries of marrow also enter the bone, make a loop and return back to where they originated from.."
"There are numerous 
in vitro studies subjecting marrow-derived mesenchymal stem cells to high hydrostatic pressures (750–75,000 mmHg) in an effort to                   induce chondrogenic phenotype.
  Even though the chondrogenic differentiation of the progenitor cells  does not take place in marrow cavity[meaning they eliminate the variable of blood loss via veins], those studies                   are related in indicating the sensitivity of the  progenitors to the magnitude and the mode (cyclic, intermittent or  static)                   of loading. In general, 
higher pressure (∼75,000 mmHg)  over lower (∼750 mmHg) and intermittent loading over static have proved                   to be more effective in chondrogenesis"<-That's quite a lot of pressure.
Here's what the author(Ozan Akkus) has to say chondrogenic differentiation not taking place in the marrow cavity:
"It is more of an opinion and the statement of an observation. We believe that this may have something to do, in part, with the mechanical environment of the marrow, that it is not conducive to chondrogenesis. Otherwise, there may be other factors in play, such as suppression by neighboring hematopoietic cells. As we know, marrow is highly vascular and cartilage is avascular. So
 the vascularity is suppressive to chondrogenesis."

 
"Layout of bone marrow in a cross-sectional view of a tubular bone. Bone (B) is surrounding the bone marrow (BM). Central artery (CA) and central vein (CV) are running parallel to each other and longitudinally along the long bone (perpendicular to the plane of the page). The central artery and central vein branch toward the periphery to form arterioles (A) and sinusoids (S) which then combine and join with the central vein. Hematopoietic space (H) is interspersed by the sinuses. Developing red blood cells and granulocytic cells appear in the hematopoietic space. Megakaryocytes develop subjacent to the endothelium of marrow sinuses. It is possible to observe the radial distribution of marrow as the yellow marrow in the central regions and the red marrow in the periphery. (b) A toluidine-blue stained section taken transversely to the longer axis of a tubular bone. The micrograph displays the endosteal junction between bone and marrow (125×). The distribution of abundant number of red blood cells indicates that the bone marrow is hematopoietic"<-this is the cortical bone however and we are looking to induce new growth plates in the epiphysis.
Dynamic compression stimulates proteoglycan synthesis by mesenchymal stem cells in the absence of chondrogenic cytokines.
"Dynamic  compression was applied to agarose hydrogels seeded with bone  marrow-derived adult equine MSCs. In the absence of the chondrogenic  cytokine transforming growth factor beta (TGFbeta), dynamic compression  applied for 12 h per day led to significantly greater proteoglycan  synthesis than in unloaded TGFbeta-free cultures, although at a rate  that was approximately 20% to 35% of unloaded TGFbeta cultures. 
These  data suggest that the emergence of aggrecan dominated a chondrogenic  response to loading as increases in proteoglycan synthesis.  Cross-sectional analyses were conducted to subjectively identify  potential spatial distributions of heterogeneous differentiation. In  loaded samples, 
cell viability and metachromatic staining was low near  the porous compression platen interface but increased with depth[the increase in depth relates to hydrostatic pressure as the more depth the larger the HP],  reaching levels in the lower portion of the hydrogel that resembled  unloaded TGFbeta cultures. These results suggest that the 
combination of  high hydrostatic pressure and low dynamic strain and fluid flow had a  stronger effect on chondrogenesis than did low hydrostatic pressure  coupled with high dynamic strain and fluid flow. Next, the 12-h per day  loading protocol was applied in the presence of TGFbeta. 
Biosynthesis in  loaded cultures was less than in unloaded TGFbeta samples[so perhaps you don't want to increase TGF-Beta levels when joint loading]. Taken  together, these data suggest that the 
duration of loading necessary to  stimulate mechanoinduction of MSCs may not be optimal for neo-tissue  accumulation in the presence of chondrogenic cytokines[but maybe higher levels of TGF-Beta just mean loading has to be applied for a shorter period of time]."
"quantitative extracellular matrix (ECM) synthesis studies have  demonstrate that MSCs are capable of synthesizing neo-tissue on the  order of that reported for chondrocyte culture."<-The MSCs in the bone marrow are capable of forming new growth plates(which is a chondrocyte culture).
"Dynamic hydrostatic loading[hydrostatic loading is performed by submerging a compound deeper under water], on the order of what occurs during routine joint functioning, has been proven to upregulate chondrogenic gene expression and cartilage-like protein synthesis in the presence of TGFβ."
"Experiments used a sinusoidal dynamic compression protocol of 2.5% strain amplitude superimposed on a 7.5% static offset strain at a frequency of 0.3

Hz in displacement control; these loading parameters are within the physiological range of moderate, low-amplitude strain when applied to intact cartilage explants. At the initiation of loading, these parameters created maximum stress response of approximately 2

kPa[a Kilopascal is 1000 of a MegaPascal, usually Hydrostatic Pressure is measured in MPa so the pressure range was well below typical Hydrostatic pressure].
For loading in the absence of TGFβ, two dynamic compression duty cycles were explored. The first protocol was defined by 6-h cycles consisting of 
45-min periods of compression followed by 5 h and 15
h and 15 min of free-swelling culture
min of free-swelling culture[I don't think we'd be able to mimic this cycle]. Each 6-h cycle was applied four times, followed by 24

h of free-swelling culture such that loading was applied on alternate days. In the second protocol, 45

min of dynamic compression was followed by 45

min of free-swelling culture throughout the loading period, resulting in 12

h of loading per day. In the presence of TGFβ, MSC-seeded agarose samples were loaded using the second, 12-h/d dynamic compression protocol."
"Given the low levels of biosynthesis in adult equine MSC cultures in the absence of TGFβ[In alternate day loading], these effects of dynamic compression were considered negligible."  So during LSJL, the loading likely has to be performed at least daily.
"H-proline and S-sulfate incorporation in dynamic compression samples were 20% of those of TGFβ+ samples (
p
<

0.05), whereas GAG accumulation in loaded cultures was 34% of that in TGFβ+ samples"<-this was twelve hours a day.
"Adjustment of the frequency of the applied loading from alternate day to daily loading, applied over 12

h/d,  resulted in significantly greater proteoglycan synthesis than in TGFβ−  cultures. These data suggest a chondrogenic response to loading because  the emergence of aggrecan production, the major proteoglycan in cartilage, probably dominates S-sulfate  incorporation and GAG accumulation. Therefore, the duration of the  application of loading appeared to be a critical factor in stimulating  proteoglycan synthesis, as occurs during chondrogenesis."<-So sustained loading may work in the presence of low pressure
  
"In the three dynamic compression samples, the zones near the chamber  base contained the highest density of viable cells, suggesting that  chondrogenesis was preferentially stimulated in deep zones of maximal  hydrostatic pressure."
"The decrease in ECM synthesis and accumulation demonstrated an inhibitory effect of loading in TGFβ."
"Previously, finite element analyses have predicted compression-induced hydrostatic pressures of less than 1

kPa in agarose constructs compressed using near-physiological deformation levels. Although this value is significantly less than that measured in joints during normal activities, it is closer to the 0 to 3

kPa reported for continuous passive motion."<-Normal motion involves 0 to 3 kPa.  So, if you walked for 12 hours a day at 3 kPascals you might be able to grow taller?
We're not going to be able to perform loading for the periods of time in this study but hopefully we're performing our stimulus at a pressure much higher than 2 kPa so we can do the loading perhaps 1/500th of the time for 1 MPa.