First-principles density functional calculations have been performed on Li-doped ZnO using all-electron projector augmented plane wave method. Li was considered at six different interstitial sites (Lii), including anti-bonding and bond-center sites and also in substitutional sites such as at Zn-site (Lizn) and at oxygen site (Lio) in the ZnO matrix. Stability of LiZn over Lii is shown to depend on synthetic condition, viz., LiZn is found to be more stable than Lii under O-rich conditions. Hybrid density functional calculations performed on LiZn indicate that it is a deep acceptor with (0/-) transition taking place at 0.74 eV above valence band maximum. The local vibrational frequencies for Li-dopants are calculated and compared with reported values. In addition, we considered the formation of Li-pair complexes and their role on electronic properties of ZnO. Present study suggests that at extreme oxygen-rich synthesis condition, a pair of acceptor type LiZn-complex is found to be stable over the compensating Lii + LiZn pair. The stability of complexes formed between Li impurities and various intrinsic defects is also investigated and their role on electronic properties of ZnO has been analyzed. We have shown that a complex between LiZn and oxygen vacancy has less formation energy and donor-type character and could compensate the holes generated by Li-doping in ZnO.