Significant research effort has focused on improving the specific energy of lithium-ion batteries for emerging applications, such as electric vehicles. Recently, a rock salt-type Li4Mn2O5 cathode material with a large discharge capacity (~350 mA·hour g-1) was discovered. However, a full structural model of Li4Mn2O5 and its corresponding phase transformations, as well as the atomistic origins of the high capacity, warrants further investigation. We use first-principles density functional theory (DFT) calculations to investigate both the disordered rock salt-type Li4Mn2O5 structure and the ordered ground-state structure. The ionic ordering in the ground-state structure is determined via a DFT-based enumeration method. We use both the ordered and disordered structures to interrogate the delithiation process and find that it occurs via a three-step reaction pathway involving the complex interplay of cation and anion redox reactions: (i) an initial metal oxidation, Mn3+→Mn4+ (Li x Mn2O5, 4 > x > 2); (ii) followed by anion oxidation, O2-→O1- (2 > x > 1); and (iii) finally, further metal oxidation, Mn4+→Mn5+ (1 > x > 0). This final step is concomitant with the Mn migration from the original octahedral site to the adjacent tetrahedral site, introducing a kinetic barrier to reversible charge/discharge cycles. Armed with this knowledge of the charging process, we use high-throughput DFT calculations to study metal mixing in this compound, screening potential new materials for stability and kinetic reversibility. We predict that mixing with M = V and Cr in Li4(Mn,M)2O5 will produce new stable compounds with substantially improved electrochemical properties.