To meet the demands for lightweight design and high-conductivity connections in new energy vehicles, the high-quality joining of dissimilar Al/Cu metals has emerged as a critical research focus. In this study, laser welding was performed on 2 mm-thick 1060 pure aluminum and T2 copper plates. The effects of laser power (3.6–4.0 kW) and welding speed (0.9–1.5 m/min) on the interfacial microstructural evolution and mechanical properties of the lap joints were systematically investigated. The results demonstrate that the macroscopic morphology of the weld is primarily governed by heat input: excessive laser power induces transverse cracking, whereas an overly low welding speed promotes porosity. Microstructural analysis revealed that intermetallic compounds (IMCs), such as Al₂Cu, AlCu, and Al₄Cu₉, predominantly form at the interface, with their morphology and distribution varying significantly depending on the heat input. Under the optimized parameters of a 3.8 kW laser power and a 1.2 m/min welding speed, sufficient mixing of the molten Al and Cu was achieved. This promoted the formation of fine, dispersed IMCs accompanied by a continuous Al–Cu eutectic layer at the interface, yielding a maximum tensile-shear load of 1561 N. This research elucidates the intrinsic relationship between heat input and the microstructure–property correlation of Al/Cu laser-welded joints, identifying a viable process window for 2 mm-thick sheets and providing theoretical and practical guidance for joining dissimilar medium-thickness metal plates.