First results on the constitution of the ternary systems Li-Sn-C and Li-Sn-Si are presented. Extrapolation calculations from the binary boundary systems allow identifying three alloys with key compositions that yield substantial information about the ternary phase diagrams. These alloys were characterized after long-term annealing using X-ray diffraction (XRD) and differential scanning calorimetry (DSC). The XRD and DSC measurements suggest the formation of a solid solution of the isostructural phases Li5Sn2 and Li7Si3 instead of predicted three phase equilibrium in the Li-Sn-Si system. Ternary phases are not observed.