Lithium titanate (Li2TiO3) is an attractive ceramic material for various industrial applications, particularly as one of the most promising breeder blanket materials in future nuclear-fusion reactors. Previously reported studies mainly focus on sintered polycrystalline samples of Li2TiO3. Surface structure of the single-crystal form is rarely reported, although the information of surface structures and stabilities can be critical for further understanding the surface-associated processes. In this work, we perform extensive first-principles density-functional-theory (DFT) calculations to obtain the surface energies of Li2TiO3 (001) with different surface terminations. For four perfect (defect-free) Li-, O-, or LiTi-terminated (001) surfaces, Li- or O-terminated (001) surfaces can be most stable in limited chemical-potential ranges corresponding to certain experimental conditions, while a LiTi-terminated (001) surface is always unfavorable relative to Li or O terminations. By calculating the total energies of various possible configurations with surface vacancies, we determine the energetically most favorable vacancy-defected surface terminations. From the corresponding ternary phase diagram, we analyze the stability of a specific surface termination with vacancies as well as the possible formation of oxides. Our stability analysis together with DFT-simulated STM images reveals that a 1/3-monolayer-Li-terminated surface most likely corresponds to the ordered hexagonal-like pattern observed previously in STM experiments. For a 1/2-monolayer-Li-terminated surface, the most stable surface structure from our DFT calculations contrasts with previous results from an empirical-potential model.