A comprehensive theoretical analysis has been developed to study vaporization of liquid oxygen (LOX) droplets in hydrogen over a wide range of pressure. The formulation accommodates complete sets of conservation equations for both gas and liquid phases, and accounts for variable properties, thermodynamic non-idealities, and vapor-liquid phase equilibria. The model is capable of treating the entire history of a vaporizing LOX droplet, including the thermodynamic phase transition through the critical mixing point. Various distinct high-pressure effects on the droplet behavior were investigated in depth. In particular, a parametric study of the droplet lifetime as a function of the ambient pressure, temperature, and initial droplet diameter has been conducted. The droplet lifetime exhibits a strong pressure dependence and can be correlated well with the square of the initial diameter.