In this article, Coupled Eulerian–Lagrangian approach is adopted for numerical analysis. A finite element model was meticulously developed to replicate the single pass friction stir lap welding of Al–Mg-Si alloys (AA6061-T6). The numerical simulation entailed investigating the lap interface and the dynamic temperature field under two distinct sets of process parameters: a traverse speed of 41 mm/min paired with rotational speeds of 875 rpm and 1230 rpm. The simulation outcomes reveal that increasing the rotational speed amplifies the generation of frictional heat at the interface between the rotating tool shoulder and the substrate. Consequently, this increases the temperature of the stirred zone. This heightened heat input induces plastic deformation within the underlying material beneath the tool shoulder, resulting in the formation of a basin-like stirred zone. As the welding process advances, it leaves in its wake a region characterized by elevated stress levels in areas previously welded. Upon the culmination of the welding operation, the plunging region emerges as the epicenter of the highest von Mises stress. Intriguingly, a compelling congruence emerged between the temperature distributions observed in both the experimental and finite element analyses, affirming the reliability of the model. Equally noteworthy is the defect-free nature of the weld surface appearance and cross-section, signifying the success of the welding process.