An ab-initio calculation was performed using the linearized augmented plane wave method (FP-LAPW), within the framework of density functional theory (DFT), with the generalized gradient approximation GGA to calculate the structural, electronic, magnetic, thermodynamic and and thermoelectric properties of quaternary Heusler CrCoLaZ alloys (Z = Ga, Si) which are of technological interest in the field of spintronics research. Calculations show that CrCoLaZ (Z = Ga, Si) compounds having characteristics of ferromagnetic half-metal with a gap of 0.6 eV. Using the quasi-harmonic Debye model, the variations of lattice parameter, thermal expansion coefficient, heat capacities and Debye temperature with pressures covering the 0–20 GPa interval and temperatures ranging from 0 to 1200 K were also investigated and in-depth discussed. The results of our simulation have been interpreted and compared to the theoretical results available. Furthermore, BoltzTrap package is used to compute thermoelectric parameters sush as density of states, Seebeck coefficient S, electrical conductivity (σ/τ), electronic thermal conductivity (κ/τ) and the figure of merit (ZT). These parameters are computed at three different temperature ranges 300, 500 and 800 K to explore the potential of these compounds for high-performance technological applications.