Commercialization of lithium-oxygen batteries faces many challenges, such as electrolyte decomposition, short cycle life, low energy and power density, and high cell mass. However, the commercialization of LiO2 batteries for aeronautics is more challenging due to additional safety constraints on cyclability and performance (high specific-power and specific-energy). In this paper, we perform experiments and use the results to calibrate a 1-D finite element model to simulate discharge profiles up to 5 mA cm-2. The calibrated model is used to perform parametric studies of geometrical, microstructural, transport, and material properties for different discharge times, and discharge current densities. Next, a simulation-based optimization study shows optimal cell designs for various electrolytes for high specific-power. Results show that a high specific-power LiO2 cell needs to have a cathode with a thickness equal to oxygen diffusion length, thin separator, optimized anode, and other components with low mass. The specific-power is sensitive to discharge time, discharge current density, and microstructural and geometrical properties. Also, in some cases, electrolytes with high oxygen solubility or high external partial pressure can compensate for electrolytes with low oxygen diffusivity. However, reducing the cell mass is the most straight forward path to improving specific-power.