The electronic structure of the new series of intermetallic compounds LnNiZBzC (Ln = lanthanide element) is calculated and discussed in terms of local chemical bonding in order to elucidate how superconductivity may be possible for some of these materials. The Fermi level occurs in a region that allows for a second-order Jahn-Teller mixing and can contribute to significant electron-phonon coupling in these systems. Moreover, the trend in the a lattice parameter for different Ln cations shifts the position of the x2-y2 band, which significantly changes its occupation and affects the superconducting transition temperature. We also compare the electronic structures of LnNizBzC with those from the related compounds LnNiBC.