Li-nanotube systems can substantially improve the capacity of Li-ion batteries by utilizing both nanotube exteriors and interiors. Our ab initio simulations show that while Li motion through the sidewalls is forbidden, Li ions can enter tubes through topological defects containing at least nine-sided rings, or through the ends of open-ended nanotubes. Once inside, their motion is not diffusion limited. These results suggest that "damaging" nanotube ropes by either chemical or mechanical means will yield superior material for electrochemical storage.