This study presents a novel time-varying mesh stiffness (TVMS) model for orthogonal face gear pairs with installation errors, incorporating the effects of elastohydrodynamic lubrication (EHL). First, tooth surface equations for point-contact orthogonal face gears are derived using the tooth surface generation principle. Through loaded tooth contact analysis (LTCA), the equivalent curvature radius, load distribution, and entrainment velocity are systematically analyzed to characterize the meshing behavior. The EHL governing equations are then solved via the progressive mesh densification (PMD) method to determine the oil film thickness on gear tooth surfaces. By applying the deformation compatibility condition, the TVMS of face gears with installation errors is calculated throughout the meshing cycle. Finally, the influences of axis intersection angle error, axis intersection error, and axial displacement error on TVMS are quantified and discussed.