Li-based quaternary Heusler LiHfPdZ (Z = Al, Ga, and In) compounds have been investigated for their electronic properties, structural stability, phonon spectra, and thermoelectric performance. Band structure calculations based on Density Functional Theory, show the indirect semiconductor nature of LiHfPdZ (Z = Al, Ga, and In) compounds with band gaps of 0.73 eV, 0.79 eV, and 0.58 eV, respectively. We obtained flat Hf-5d bands (without dispersion) in the vicinity of Fermi energy (EF), resulting in a high value of Seebeck coefficient. The positive values of frequencies in the phonon dispersion curve confirm the dynamic stability of these compounds. The computed elastic properties suggested that the studied compounds are mechanically stable. The calculated values of melting points of this compounds are around 1500 ± 300 K, which ensures the stability of these compounds at high temperatures. We obtained a maximum value of the figure of merit 0.72, 0.68 and 0.67 for LiHfPdAl, LiHfPdGa and LiHfPdIn compounds respectively, which is higher than other Li based QH compounds of same kind i.e. LiHfCoSn (0.59) and LiHfCoGe (0.61) obtained by Singh et al. at same temperature. Overall, a comparatively high and stable value of ZT above 600 K is obtained only in LiHfPdAl, which suggests that it is the most suitable candidate as TE material for high-temperature applications.