Using density functional theory (DFT) the first-principles calculations are employed to systematically investigate the effect of hydrostatic compression on the structural, elastic, electronic, thermal and thermodynamic properties of ternary silicides Li2TmSi3 (Tm = Ir, Pt, Rh, Os) with the ground-state optical features. The gradual decrease of bond length, unit cell volume and a smooth change of c/a with pressure deny the possibility of pressure induced phase transition up to 50 GPa. All the compounds studied here are mechanically stable within the considered pressure range. The constants C11, C12, C13 and C33 exhibit an almost linear increase trend with increase of pressure, while C44 shows anomalous behavior. The bond-stretching and bond-bending force constants are calculated based on the data of elastic constants and their pressure dependent behavior are discussed. Hydrostatic pressure enhances the inherent elastic anisotropy of Li2TmSi3. The ternary silicides studied here cannot be easily compressed under uniaxial stress. The atomic bonds between the nearest neighbors along [001] direction are stronger than those along [100] direction in the whole range of pressure. All ternary silicides except Li2PtSi3 are brittle in nature at ambient pressure. Under elevated pressure all studied compounds show brittle to ductile transition except Li2PtSi3 that exhibits brittle nature under 10 GPa. The shear modulus of Li2OsSi3 shows anomalous change under pressure, which may be attributed from its anomalous change of θD. The higher melting point of all silicides implies that they might have possible uses in harsh environments. The TDOS at EF in Li2TmSi3 decreases almost linearly with pressure. Pressure and temperature dependent thermodynamic properties and ground-state optical functions are described with implications, which may be supportive for further investigation of these compounds through experiments and theories.