Using first-principles calculations based on density functional theory, the structural, electronic and thermodynamic properties of Li2CdGeS4 and Li2CdSnS4 compounds are investigated. We confirmed that both Li2CdGeS4 and Li2CdSnS4 are diamond-like semiconductors of the wurtzstannite structure type based on that of diamond in terms of tetrahedra volume. All the tetrahedra are almost regular with major distortion from the ideal occurring in the LiS4 tetrahedron, with values for S-Li-S ranging. from 105.69 degrees to 112.84 degrees in the Li2CdGeS4 compound. Furthermore, the Cd-S bond possesses a stronger covalent bonding strength than the Li/Ge-S bonds. In addition, the inter-distances in Li2CdSnS4 show a larger spread than the distances in the Li2CdGeS4 compound. The electronic structures have been calculated to understand the bonding mechanism in quaternary Li-containing chalcogenide diamond-like semiconductors. Our results show that Li2CdGeS4 and Li2CdSnS4 are semiconductors with a direct band gap of 2.79 and 2.42 eV and exhibit mixed ionic-covalent bonding. It is also noted that replacing Ge by Sn leads to a decrease in the band gap; this behavior is explained in terms of bond lengths and electronegativity differences between atoms. Optical properties, including the dielectric function, reflectivity, and absorption coefficient, each as a function of photon energy are calculated and show an optical anisotropy for Li2CdGeS4 and Li2CdSnS4. The static dielectric constant epsilon(1)(0) and static refractive index n(0) decrease when Ge is replaced by Sn. The influence of pressures and temperatures on the thermodynamic properties like the specific heat at constant volume C-v, and at constant pressure C-p, the Debye temperature Theta(D), the entropy S and the Gruneisen parameter gamma have been predicted at enlarged pressure and temperature ranges. The principal aspect from the obtained results is the close similarity of both compounds.