Laser beam powder bed fusion (PBF-LB) additive manufacturing (AM) is an advanced manufacturing technology that manufactures metal components in a layer-by-layer manner. The thermal residual stress (RS) induced by the repeated heating–melting–cooling–solidification processes of AM is considered to limit the wider uptake of PBF-LB. A dual-laser beam PBF-LB strategy, with an additional auxiliary laser and reduced power, working in the same powder bed simultaneously, was recently proposed to lower RS within the manufactured components. To provide insights into the optimum PBF-LB AM configurations and process parameters for dual-laser PBF-LB, this study proposed three different coordinated heating strategies (i.e., parallel heating, post-heating, and preheating) of the auxiliary heat source. The temperature fields and RS of dual-laser beam PBF-LB, for Ti-6Al-4V with different process parameters, were computationally investigated and optimized by the thermo-mechanically coupled 3D models. Compared with the single beam PBF-LB, parallel heating, post-heating, and post-heating strategies were proved as effective approaches to reduce RS. Among these, the preheating scanning is predicted to be more effective in mitigating RS, i.e., up to a 10.41% RS reduction, compared with the single laser scanning. This work could be beneficial for mitigating RS and improve the mechanical properties of additively manufactured metal components.