The presence of liquid crystalline phases in suspensions of solid lipid nanoparticles can increase the risk of their gelling upon administration through fine needles. Here we study the formation of liquid crystalline phases in aqueous suspensions of platelet-like shaped solid lipid nanoparticles. A native lecithin-stabilized trimyristin (20 wt %) suspension was investigated at different dilution levels by small-angle X-ray scattering (SAXS) and visual inspection of their birefringence between two crossed polarizers. For trimyristin concentrations phi(MMM) < 6 wt %, the dispersed platelets are well separated from each other whereas they start to self-assemble into stacked lamellae for 6 wt % <= phi(MMM) < 12 wt %. For phi(MMM) >= 12 wt %, the SAXS patterns become increasingly anisotropic, which is a signature of an evolving formation of a preferred orientation of the platelets on a microscopic scale. Simultaneously, the suspensions become birefringent, which proves the existence of an anisotropic liquid crystalline phase formed in the still low viscous liquid suspensions. Spatially resolved SAXS scans and polarization microscopy indicate rather small domains in the (sub)micrometer size range in the nematic liquid crystalline phase and the presence of birefringent droplets (tactoids). The observed critical concentrations for the formation of stacks and the liquid crystalline phase are significantly higher as for equivalent suspensions prepared from triglycerides with longer chains. This can be explained with the lower aspect ratio of trimyristin platelets. Special emphasis is put on the isotropic-liquid crystalline phase transition as a function of the ionic strength of the dispersion medium and phi(MMM). Higher salt concentrations allow shifting of the phase transition to higher trimyristin concentrations. This can be attributed to a partial screening of the repulsive forces between the platelets, which allows higher packing densities within the platelet stacks and of remaining isolated platelets.