Li-rich cathode is one of the promising high capacity energy storage for future applications. While layered Lirich cathodes are studied the most, they are susceptible to phase transformation when Li is depleted. To address this problem, $\beta-Li_2MO_3$ (M = transition metal) have been considered because three-dimensionally connected transition metals can prevent the phase transformation. However, only $\beta-Li_2IrO_3$ has been reported. Therefore, first of all, we systematically investigate the trend of $\beta-Li_2MO_3$ (M = 3d, 4d, or 5d transition metals) as cyclable Li-rich cathodes using electronic structure calculations. We find the charge transfer energy (or the relative band positions) computed from density of states correlates to the activity and reversibility of oxygen redox as well as voltage. Though 3d transition metal substitutions to $\beta-Li_2MO_3$ are desired economically, it promotes O-O dimer formation, indicating the irreversible phase degradation and voltage hysteresis. After that we investigated the charge transfer energy can also predict cyclability of extended chemical space considering various TM arrangement, including TM disordered structure and different Li/M composition.