The formation and mobility of Li point defects in lithium metaborate (LiBO2) are investigated theoretically with periodic quantum chemical methods. Calculated defect formation energies obtained with a density functional theory/Hartree-Fock hybrid method and with the Perdew-Wang density functional method are compared. The basis set effect is investigated by comparison of results obtained with atom-centered basis functions and plane waves. With both methods, only a moderate relaxation is observed for the atoms surrounding the Li defect position. The defect-induced change of electronic properties is investigated by calculating the density of states for the stoichiometric and defective supercells. Various pathways for Li diffusion are investigated using the climbing-image nudged elastic band (cNEB) approach. It is observed that the Li+ ion migrates along the c direction and in the xy plane. The calculated activation energies are in reasonable accordance with experiment.