Two-dimensional (2D) heterostructures are interesting candidates for efficient energy storage devices due to their high carrier capacity by reversible intercalation. We employ here density functional theory calculations to investigate the structural and electronic properties of lithium intercalated graphene/molybdenum disulfide (Gr/MoS2) heterostructures. We explore the extent to which Li intercalates at the interface formed between graphene (Gr) and molybdenum disulfide (MoS2) layers by considering the adsorption and diffusion of Li atoms, the energetic stability, and the changes in the structural morphology of MoS2. We investigate the corresponding electronic structure and charge distribution within the heterostructure at varying concentrations of Li. Our results indicate that the maximum energetically allowed ratio of Li to Mo (Li to C) is 1:1 (1:3) for both the 2H and 1T' phases of MoS2. This is double the Li concentration allowed in graphene bilayers. We find that there is 60% more charge transfer to MoS2 than to Gr in the bilayer heterostructure, which results in a maximum doping of Gr and MoS2 of n(C) = 3.6 x 10(14) cm(-2) and n(MoS2) = 6.0 x 10(14) cm(-2), respectively.