LuGe3 was obtained under high-pressure and high-temperature conditions at pressures between 8(1) and 14(2) GPa and at temperatures in the range from 1100(150) to 1500(150) K. The high-pressure phase is isotypic to DyGe3 and decomposes at ambient pressure and T = 690 K mainly into (cF8)Ge and LuGe2-x. Chemical bonding analysis of LuGe3 reveals two-center electron-deficient Ge-Ge bonds, multicenter polar Lu-Ge interactions, and lone pairs on germanium. Magnetic susceptibility, specific heat, and electrical conductivity measurements indicate transition into a superconducting state below T-c = 3.3(3) K.