The syntheses and structures of and bonding in the title compounds are described and compared with those for the isostructural orthorhombic Er7Ni2Te2 (Imm2) and other related phases. Single-crystal data are reported for Z = Ni, Pd. The condensation of tricapped trigonal prisms (TTP) into sheets and the bridging of these by separate Lu atoms into a 3D structure are described. The interlayer separation, the Lu-Lu bonding achieved, and the polar Lu-Te bonding therewith are all affected by the size and valence energies of Te. The two Te spacers also exist in capped centered Lu6Te trigonal prisms. In terms of extended Huckel band analyses, the overall bonding for both Lu-Ni and Lu-Te are optimized energetically, but not for Lu-Lu. The average Lu-Lu overlap populations about each Lu appropriately increase with a decrease in the number of its Te neighbors.