This paper introduces a multiphysical model for laser welding in a lap joint configuration with dissimilar metals. Initially solved in a 2D axisymmetric configuration for static shots, the model is extended to 3D to simulate laser welding with a weld seam formation. Heat transfer, fluid flow, and species tracking are solved with the level set method to describe dynamically the keyhole and melt pool behavior. Validation against experimental data shows an accurate description of the main phenomena. The paper mainly highlights the need of introducing a thermal contact resistance to correctly predict the melted area dimensions. The study emphasizes the importance of considering imperfect material contact and proposes an effective approach for thermal contact resistance, a phenomenon poorly discussed in the literature.