Lead-free halide perovskite materials have recently been deployed for energy storage applications such as lithium-ion batteries and photo-rechargeable batteries. Yet, the detailed interactions between the lithium ions and the lead-free halide perovskite remain elusive, inhibiting deeper understanding of the halide perovskite materials for the energy storage applications. In this manuscript, we systematically investigate the adsorption of lithium ions on an experimentally verified two-dimensional (2D) lead-free halide perovskite Cs2CuBr4 via first-principles calculations. The simulation demonstrates that the lithium ion can reside on multiple sites at the halide perovskite surface near the bromine atoms, albeit initiating severe structural distortions in the substrate. The lithium ions move relatively easily on the halide perovskite surface, which is demonstrated by the small energy barriers of 0.15 eV. The lithium substitution at the A-site of the ABX3-type halide perovskite material causes a systematic band gap reduction when more lithium ions are available. More importantly, the hole polaron formation in the Li+/perovskite systems leads to a strong displacement of the lithium ion away from the halide perovskite surface plane, suggesting the light-driven lithium ion tunneling effect and the photo-charging behavior of the 2D halide perovskite, which is a prerequisite for the photo-battery materials. Other secondary battery active species including Na+, K+, Mg+, Ca2+ and Al3+ ions adsorb onto the halide perovskite substrate in a similar way as the Li+ ion does, suggesting the possibility of applying the 2D lead-free halide perovskite materials for more types of secondary batteries. This study facilitates the fundamental understanding of the halide perovskite materials for the energy storage applications, and suggests that the 2D lead-free halide perovskite material is viable for lithium-ion batteries and photo-batteries, pending further improvement in the stability.