The structural, electronic, optical, and thermo-electric properties of LuNiBi and LuNiSb Half-Heusler have been studied using a full potential linearized augmented plane-wave (FP-LAPW) method. The results of the calculations presented in this work were obtained through the use of different approximations GGA-PBE, GGA-PBEsol, GGA-WC, and mBJ-GGA. The electronic band structures exhibit that the LuNiBi and LuNiSb alloys have a small indirect gaps in the valence band and the conduction band at points CYRILLIC CAPITAL LETTER GHE and X, revealing the semiconductor character in both compounds. The complex dielectric function epsilon (omega), optical conductivity sigma (omega), extinction coefficient k (omega), refractive index n (omega), and reflectivity R (omega) as a function of photon energy are calculated using mBJ-GGA approximation, that is yielding results in good accordance with available experimental data. On the other hand, the variations of the thermal conductivity, power factor, figure of merit ZT, Seebeck coefficient, and electrical conductivity, as a function of temperature, have been investigated. Most of the optical and thermoelectric properties of LuNiSb and LuNiBi materials are not available in the literature; this makes the present work as a detailed comparative study between both compounds and opens the path for other future accurate theoretical studies to find the promising substitute for the interesting and more efficient thermoelectric device in industry.