Calculations are performed on the free energies for proton-promoted reactions of the lithium-ion-battery electrode material LiMn(2)O(4) spinel in acid, as a function of lithium excess and lithium deficiency relative to stoichiometry. In particular, we consider the dissolution reaction proposed by Hunter (J. Solid State Chem., 1981, 39, 142), in which protons react with lithium manganate spinel to form lambda-MnO(2), Li(+), and Mn(2+) products. The calculations employ a hybrid method developed in previous work in which first principles total energy calculations are applied for the solid phases and free atom energies, and tabulated ionization and hydration energies for the aqueous species. A correction to the atomic energies, derived from analysis of binary oxide dissolution reactions, improves the accuracy of the results. A Pourbaix-like dissolution/stability phase diagram is constructed from the resultant reaction free energies.