Lithium-rich layered oxides such as Li2MnO3 have shown great potential as cathodes in Li-ion batteries, mainly because of their large capacities. However, these materials still suffer from structural degradation as the battery is cycled, reducing the average voltage and capacity of the cell. The voltage fade is believed to be related to the migration of transition metals into the lithium layer, linked to the formation of O-O dimers with a short bond length, which in turn is driven by the presence of oxygen holes due to the participation of oxygen in the redox process. We investigate the formation of O-O dimers for partially charged O1-Li2MnO3 using a first-principles density functional theory approach by calculating the reaction energy and kinetic barriers for dimer formation. Next, we perform similar calculations for partially charged O1-Li2IrO3, a Li-rich material for which the voltage fade was not observed during cycling. When we compare the stability of the oxygen framework, we conclude that the formation of O-O dimers is both thermodynamically and kinetically viable for O1-Li0.5MnO3. For O1-Li0.5IrO3, we observe that the oxygen lattice is much more stable, either returning to its original state when perturbed, or resulting in a structure with an O-O dimer that is much higher in energy. This can be explained by the mixed redox process for Li2IrO3, which is also shown from the calculated magnetic moments. The lack of O-O dimer formation in O1-Li0.5IrO3 provides valuable insight as to why Li2IrO3 does not demonstrate a voltage fade as the battery is cycled, which can be used to design Li-rich battery cathodes with an improved cycling performance.