This study investigates the stability and potential of lead-free double oxide perovskites Li2MoZO6 (Z = Si, Ge, and Sn) for solar energy harvesting. Density functional theory (DFT) calculations using the WIEN2k package reveal that all three compounds exhibit cubic symmetry (space group Fm-3m). Additionally, tolerance factor analysis, phonon spectra, formation energy calculations, and ab initio molecular dynamics simulation verified the structural, dynamic, thermodynamic, and thermal stability of the compounds at room temperature. Electronic properties calculated using the TB-mBJ and HSE06 potentials reveal that Li2MoZO6 (Z = Si, Ge, Sn) compounds exhibit semiconducting behavior, with band gaps of (1.78, 1.64, and 1.34) eV, respectively, from TB-mBJ calculations, and corresponding values of approximately (2.10, 1.85, and 1.64) eV from HSE06 calculations. Elastic constants calculations demonstrate the mechanical stability, ductility, and anisotropy of the given compounds. The analysis of optical properties reveals high absorption coefficients and significant optical conductivity within the visible and near-UV spectrum, indicating the potential applications of the simulated compounds in photovoltaic and optoelectronic.