For first time, the magneto‐electronic structure with thermoelectric and mechanical properties of lanthanum‐based double perovskite La₂CuMnO₆ are investigated, using first‐principle methods. Generalized gradient approximation and modified Becke‐Jhonson potentials are integrated to figure out exchange‐correlation potential. The alloy stabilizes in cubic structure with ferromagnetic nature and determined structural parameters are consistent with experimental results. The band profile reveals the half‐metallic character, which is further confirmed by calculated electronic conductivities of up and down spin channels. The effect of pressure on the structural and electronic profile is demonstrated here. The analysis of the transport properties portrays that the highest value of 0.39 is achieved for figure of merit at higher temperatures. The mechanical stability of La₂CuMnO₆ is established, by determination of elastic constants. The calculated elastic parameters specify the ductile behavior of alloy with high melting temperature. The efficient thermoelectric parameters with half‐metallic and ductile character suggest the likelihood of applications of alloy to design hard spintronic devices or potential thermoelectric materials.