In this research, the properties of GaN monolayer, defective GaN monolayer with N vacancies (GaN-VN), and van der Waals (vdW) heterostructures composed of them and graphene (GaN/graphene, GaN-VN/graphene) are systematically investigated using density functional theory (DFT), which includes assessment of the structure's stability, mechanical property, electronic structure analysis, lithium adsorption and diffusion properties, maximum theoretical capacity, and average open-circuit voltage. The calculations show that two-dimensional GaN transforms from semiconductor to metal by forming nitrogen-vacancy defects. This increases lithium adsorption performance while ensuring rapid electron motion in the electrode during lithium adsorption and removal processes. The synergistic effect between the heterostructure layers and the presence of the built-in electric field improves the electron and ion conductivity and lowers the migration energy barriers. In addition, the maximum theoretical capacities of defective GaN-VN, GaN/graphene, and GaN-VN/graphene can reach 970 mAh/g, 884 mAh/g, and 890 mAh/g, respectively, far exceeding those of the conventional graphite anode material (372 mAh/g). The above advantages indicate that defective GaN-VN, GaN/graphene, and GaN-VN/graphene are potential replacements for lithium-ion battery anodes.