This article presents a comprehensive numerical analysis of liquid oxygen (LOX) droplet vaporization in quiescent hydrogen and water environments over a broad range of ambient conditions. The theoretical formulation is based on a complete set of conservation equations of mass, momentum, energy, and species concentrations in a spherically symmetric coordinate. A self-consistent and efficient method for evaluating transport properties and a unified treatment of general fluid thermodynamics are incorporated into an implicit finite-volume numerical scheme. The analysis is further equipped with a water-vapor condensation model for treating the phase change near the droplet surface. The effects of the Dufour and Soret cross-diffusion terms are explored and found to exert negligible influences on the droplet lifetime. Various issues associated with high-pressure droplet vaporization are investigated. In addition, correlations for droplet lifetimes are established for both LOX/hydrogen and LOX/hydrogen/water systems in terms of the initial droplet diameter, reduced critical temperature of oxygen, and thermal conductivities of oxygen and ambient gases.