This study aims to investigate the numerical behaviors of the mixed lubrication model in point contact and three-dimensional (3D) line contact based on the non-normalized discretization, in which the dimensional Reynolds equation is discretized according to the full analysis of the pressure balance. The solution is iteratively obtained from an initial value by the analysis of the dry contact and the model is capable of both the steady-state and the time-dependent lubrication in a large range of entrainment velocity. The transient solutions of the startup and shutdown processes in point contacts are compared with those experimentally measured and good consistency is achieved, and effects of the time intervals on lubrication evolution are numerically investigated. The algorithm developed in this study enables its application for the elliptical lubrication without ellipticity parameters specified. The contact of a roller with a flat surface is presented to demonstrate the generality of the point-contact model and the effects of roughness orientation are also revealed. The numerical errors of the 3D-line lubrication brought by the formulation of the solution matrix are then discussed in detail, comparing with the solutions of the two-dimensional (2D) lubrication model. It is concluded that the hydrodynamic effect along the extending direction plays an important role in the lubrication when surfaces with transversely oriented roughness are concerned and the 3D model may provide a more reasonable solution. The 2D lubrication model, nevertheless, may provide a relatively accurate solution along a specified line for the longitudinal roughness while consuming less computational time.