It will get entirely unusual derivatives with gratifying chemical bonding schemes for boron clusters by doping with lithium, the lightest alkalis. The geometric structures and electronic properties of the LiBn0/- (n = 10-20) clusters have been studied through Crystal structure AnaLYsis by Particle Swarm Optimization (CALYPSO) structural search approach along with the density functional theory (DFT) calculations. The low-lying candidates of LiBn0/- (n = 10-20) are reoptimized at the B3LYP functional in conjunction with 6-311 + G(d) basis set. Three forms of geometric configurations are identified for the ground-state structures of LiBn0/- clusters: half-sandwich-type, quasi-planar and drum-type structures. The photoelectron spectra (PES) of the LiBn- clusters have been calculated through time-dependent density functional theory (TD-DFT). A promising LiB13 with tetrahedral-typed B13 ligand half-surround cluster and robust stability is uncovered. The molecular orbital and adaptive natural density partitioning (AdNDP) analysis show that B-B bonds in the B13 moiety combined with the interaction between the B13 shell and Li atom stabilize the C2v LiB13 cluster. Our results advance the fundamental understanding about the alkali metal doped boron clusters.