We studied the structural, electronic, phonon spectrum and thermoelectric properties of ternary LuMSb (M = Ni, Pd, Pt) half Heusler compounds by using first principles method. The electronic properties are calculated via energy band structure and density of states by using GGA + U approximation. The calculations reveal that the replacement of Ni with Pd and Pt, energy gap decreases and LuNiSb, LuPdSb are found to have narrow indirect band gaps and exhibit semiconducting nature, while LuPtSb is found to be a gapless semiconductor. Phonon band structure calculations give only positive values of phonon frequency indicating the dynamically stability of these compounds. The thermoelectric properties have been computed using semi‐classical Boltzmann transport theory. We found high Seebeck coefficient (S) and high power factor (PF) for LuNiSb and LuPdSb compounds in the whole temperature range. The ZT values of LuNiSb and LuPdSb are high in general and reach a maximum of 0.67 and 0.69 at 450 K, respectively, whereas 0.39 is the maximum ZT value for LuPtSb at the same temperature. These findings propose LuNiSb and LuPdSb compounds as promising materials for thermoelectric applications at room temperature. [ABSTRACT FROM AUTHOR]