We introduce a novel numerical model that integrates a Boundary Element Method (BEM) code in Fourier space to solve the problem of lubricated frictional contact between rough surfaces. This model accounts scenarios where the lubricant quantity is significant yet discontinuous, leading to the formation of trapped, compressible lubricant pockets at the contact interface. Additionally, it incorporates the plastic behavior solid surfaces through a simple plastic saturation method, enabling comprehensive analysis of contact area, pressure distribution, and variations in the friction coefficient across a wide range of conditions, such lubricant type, density, and surface roughness. Comparison with experimental strip-drawing tests shows that, despite its simplicity, the model successfully captures the observed trend of a decreasing friction coefficient with increasing normal pressure in a mixed lubrication regime. Notably, the study reveals that when the amount of lubricant is insufficient to fully fill interfacial gap, even minor adjustments in its distribution can significantly influence the friction behavior aluminum during forming processes.