This study uses density functional theory to investigate the structural, mechanical, electronic, optical, and thermodynamic properties of tetragonal LaRhGe3, LaIrGe3, and LaPdGe3 compounds. The investigated lattice parameter showed similar results to the experimental data, justifying the accuracy of our calculations. The negative values of formation enthalpy confirmed the thermodynamic stability of LaTGe3 (T = Rh, Ir, or Pd). The mechanical stability of these compounds was also verified by their single independent elastic constants. Poisson’s and Pugh’s ratios revealed that all the compounds have a ductile nature. The metallic nature of these phases was found from their band structure calculations. The study of Mulliken bond populations and charge density maps ensured the existence of a mixed character of ionic, covalent, and metallic nature in LaRhGe3, LaIrGe3, and LaPdGe3 compounds. Detailed investigation was also performed on optical properties, and the dielectric function, absorption, and conductivity again ensured the metallic feature of all these phases. The calculated optical functions suggested their potential application in quantum-dot light emitting diodes, organic light emitting diodes, solar cells, waveguides, and solar heating reduction. Moreover, the very low values of minimum thermal conductivity and the Debye temperature are indicative of their suitability for thermal barrier coating materials.