The KKR (AkaiKKR software package) and FLAPW (Elk software package) methods were used to model the structural, thermodynamic, energetic, and electrokinetic characteristics of the Lu1-xZrxNiSb semiconductor solid solution. It is shown that defects of acceptor nature are present in the structure of LuNiSb as a result of vacancies in positions 4a and 4c of Lu and Ni atoms, respectively, which generates two acceptor levels ^V_A^ac4 a and ^V_A^ac4^c in the band gap εg. When Zr atoms are introduced into the LuNiSb structure by replacing Lu atoms in position 4a, Zr atoms also occupy vacancies in this position, which increases the lattice parameter a(x) and eliminates defects of acceptor nature and corresponding acceptor levels When the vacancies are filled, Lu atoms are displaced, which reduces the value of the unit cell parameter and generates defects of donor nature and donor levels _D^{4 a} . The Ni atoms return to position 4c, which increases the a(x) value and eliminates defects of acceptor nature and the corresponding acceptor levels ^V_A^ac4^c . At the lowest concentration of Zr atoms, the conduction type of Lu1-xZrxNiSb changes from p- to n-type. The simulation results are consistent with experimental studies of Lu1-xZrxNiSb.