This study evaluates the possibility of applying a novel meshless Fragile Points Method (FPM) for solving Reynolds’ equation in lubrication theory, comparing its performance with available analytical solutions and established numerical methods, namely the Finite Difference Method (FDM) and the Finite Element Method (FEM). Reynolds’ equation is solved in one and two dimensions, considering different hydrodynamically lubricated conformal and non-conformal contacts, and including smooth and rough surfaces with artificial and realistic surface roughness profiles or topographies. The results demonstrate that FPM can be successfully applied for solving Reynolds’ equation, with accuracy comparable to FDM and FEM over the considered contacts, surface roughnesses and mesh resolutions. The ability of FPM to efficiently handle sharp transitions in applications with irregular surface features or micro-textured contacts—particularly at low mesh resolutions—without significant loss of accuracy underscores its potential for solving complex multiphysics tribological problems. These problems may involve structural mechanics, heat transfer, and crack propagation, areas in which FPM has already been successfully applied.