The porosity of the cathode in a lithium-oxygen battery is a crucial parameter that influences oxygen transport and active surface area availability. This study explores various cathode models with different initial porosity distributions and analyses the porosity evolution during discharge. The objective is to maximize the active surface area utilization of the cathode and increase the battery's discharge capacity. The simulations employ a recently developed Lattice Boltzmann method (LBM) model proposed by Chen et al. (Chen, S., B. Yang, and C. Zheng, Simulation of double-diffusive convection in fluid-saturated porous media by lattice Boltzmann method. International Journal of Heat and Mass Transfer, 2017. 108: p. 1501-1510.), which is capable of handling spatial and temporal variations in diffusion coefficient values. The results demonstrate that a hierarchical porous cathode provides a better specific capacity than a uniform porous cathode with the same average initial porosity. The specific capacity increases as the magnitude of initial porosity variation in the domain increases. Furthermore, incorporating oxygen channels improves oxygen transport in the cathode and offers a better specific capacity than the hierarchical porous cathode. A combination of hierarchical porous media and oxygen channels delivers the best specific capacity among all the other cathode models, as it efficiently balances oxygen transport and active surface area.