Aqueous suspensions of platelet-like shaped tripalmitin nanocrystals are studied here at high tripalmitin concentrations (10 wt % tripalmitin) for the first time by a combination of small-angle X-ray and neutron scattering (SAXS and SANS). The suspensions are stabilized by different lecithins, namely, DLPC, DOPC, and the lecithin blend S100. At such high concentrations the platelets start to self-assemble in stacks, which causes interference maxima at low Q-values in the SAXS and SANS patterns, respectively. It is found that the stack-related interference maxima are more pronounced for the suspension stabilized with DOPC and in particular DLPC, compared to suspensions stabilized by S100. By use of the X-ray and neutron powder pattern simulation analysis (XNPPSA), the SAXS and SANS patterns of the native tripalmitin suspensions could only be reproduced simultaneously when assuming the presence of both isolated nanocrystals and stacks of nanocrystals of different size in the simulation model of the dispersions. By a fit of the simulated SAXS and SANS patterns to the experimental data, a distribution of the stack sizes and their volume fractions is determined. The volume fraction of stacklike platelet assemblies is found to rise from 70% for S100-stabilized suspensions to almost 100% for the DLPC-stabilized suspensions. The distribution of the platelet thicknesses could be determined with molecular resolution from a combined analysis of the SAXS and SANS patterns of the corresponding diluted tripalmitin (3 wt %) suspensions. In accordance with microcalorimetric data, it could be concluded that the platelets in the suspensions stabilized with DOPC, and in particular DLPC, are significantly thinner than those stabilized with S100. The DLPC-stabilized suspensions exhibit a significantly narrower platelet thickness distribution compared to DOPC- and S100-stabilized suspensions. The smaller thicknesses for the DLPC- and DOPC-stabilized platelets explain their higher tendency to self-assemble in stacks. The finding that the nanoparticles of the suspension stabilized by the saturated lecithin DLPC crystallize in the stable beta-tripalmitin modification with its characteristic platelet-like shape is surprising and can be explained by the fact that the main phase transformation temperature for DLPC is, as for unsaturated lecithins like DOPC and S100, well below the crystallization temperature of the supercooled tripalmitin emulsion droplets.