Atomistic simulation methods are used to investigate lithium and proton insertion in spinel lithium manganates, The energetics of lithium extraction and reinsertion by redox reactions in the LiMn2O4-lambda-MnO2 system are evaluated with respect to the formation of lithium vacancies or interstitials and to overall changes in lattice energy. Lithium migration mechanisms are also investigated, considering the energies for Li+ ions to migrate through different pathways in the interstitial space of the lattice. The local structures around Mn 16d vacancies in spinels of composition LiMn2O4+delta and Li1+xMn2-xO4 are modeled to determine the effects of the vacancies on Lithium and proton sites. Possible orientations of hydroxyl groups formed by inserted protons in the structure are examined, and a strong energetic preference for the hydroxyl groups to coordinate the 16d vacancies is found. A model is proposed for protonated spinel MnO2 in which four hydroxyl groups are symmetrically distributed in planar configuration around each 16d vacancy.