As a geochemical tracer in mantle studies, lithium isotopes play an important role in diffusion and fractionation in major mantle minerals. Olivine and its high-pressure phases, wadsleyite and ringwoodite, are considered to predominate in the upper mantle and transition zone on the earth. We carried out simulations of lithium isotopes' diffusion and fractionation in Mg end member olivine and its high-pressure phases to learn the details of the signatures of lithium isotopes preserved in mantle materials. In this work, the diffusion and fractionation mechanisms between different lattice sites of lithium isotopes in forsterite (Mg2SiO4), wadsleyite (-Mg2SiO4) and ringwoodite (-Mg2SiO4) at the atomic level are studied using empirical atomistic simulation techniques. It is found that Li can pass through the high-pressure phases (wadsleyite and ringwoodite) energetically much easier due to the low migration energy barriers via either substitutional or interstitial mechanism. The activation energy is high for Li diffusion along the interstitial path in the forsterite and decreases drastically with the assist of Mg vacancies. The temperature-dependent fractionation for two Li isotopes between two different lattice sites is calculated at the temperatures from 300 to 2500K. This behavior generates the lighter Li storage in the near-surface mantle-derived rocks and provides insights into zoning and composition of lithium isotopes in olivine and its high-pressure phases.