We report a comprehensive and complementary study on structural, elastic, mechanical, electronic, phonon, and electron-phonon interaction properties of LaX 3 (X = In, Pb, and Bi) using first-principles density functional calculations within the local density approximation with and without the spin-orbit coupling (SOC). The calculated lattice parameters for these intermetallic compounds with and without SOC are found to differ by less than 2% from their experimental values. The effect of SOC on the elastic, mechanical, electronic, phonon, and electron-phonon interaction properties is more profound for LaPb 3 and LaBi 3 containing heavier X elements rather than LaIn 3 containing lighter X element. The inclusion of SOC considerably removes the degeneracies of some bands near the Fermi level and makes some phonon branches in LaPb 3 and LaBi 3 softer and increases the strength of dominant peaks in their Eliashberg spectral functions. Thus the SOC related enhancement of their electron-phonon coupling parameter values can be related to both a softening of their phonon dispersion curves and an increase in their electron-phonon coupling matrix elements. The superconducting transition temperature with SOC is computed to be 0.69 K for LaIn 3 , 4.23 K for LaPb 3 , and 6.87 K for LaBi 3 , which agree very well with the respective measured values of 0.70, 4.18, and 7.30 K.