Structural growth mechanism, energetics, and electronic properties of cationic, neutral, and anionic lutetium doped germanium cluster LuGe_n^(+/0/-) (n = 6～19) were comprehensively studied by the ABCluster unbiased global search technique with a hybrid density functional theory approach. Compared to the experimental PES, the anion evolution of structure can be clearly defined as four-phase: from the adsorbed to the link structure, then to the half cage motif, and finally to the endohedral structure. The results revealed that the LuGe₁₆^- as Frank-Kasper structure with high symmetry of T_d can greatly enhance the stabilities. Doped structures have shown thermodynamic stability and appropriate energy gap. These materials are suitable semiconductors. Various approaches, including quasi-spherical geometry with closed-shell model, aromaticity, UV-Vis spectra, density of states (DOS) and partial density of states (PDOS) were applied to further support the results.