The first principles study of Transition Metal Chalcogenides LiMS (M = Cu, Ag) has been conducted utilizing the concepts of Density Functional Theory (DFT). Both the compounds possess a cubic structure with space group F-43m. The mechanical stability of LiCuS and LiAgS has been predicted based on the values of elastic tensor. These Chalcogenides possess an interesting electronic band structure which reveals their semiconducting nature with a direct band gap. The electronic structure is further subjected to high pressure and the changes in band gap are deeply observed. For these materials, the changes in band gap in response to applied pressure suggest the possibility of their use in band gap engineering. The phonon curves are investigated over the Brillouin zone's high symmetry directions which reveal the lattice dynamical stability of the presently studied compounds. Moreover, the atoms present at different positions inside a crystal lattice exhibit vibrations of different intensities and in different directions which have been studied through the Eigenvector representations. The thermoelectric properties of LiCuS and LiAgS have been characterized using Boltzmann's theory over the range of temperature between 100 K and 1600 K. The calculated thermoelectric parameters reveal the high thermoelectric efficiency of these materials with excellent values of the figure of merit. The interesting properties of ternary Chalcogenides LiMS (M = Cu, Ag) make them promising candidates for thermoelectric applications.