Metal additive manufacturing (AM) has attracted significant attention in various industry sectors for large-scale fabrication. However, the limited fabrication efficiency has hindered its practical implementation. In comparison to traditional methods of tuning process parameters, concurrent AM equipped with multiple independently driven lasers is a more promising technique recently developed for the efficient fabrication of large metal parts. To maximize fabrication efficiency while ensuring quality for multi-laser AM processes, an optimization problem is proposed in this work for multi-laser scanning plan, including scan vector assignment and scheduling. The goal is to minimize the makespan while considering factors that may affect the quality of metal AM parts as constraints. Specifically, the constraints associated with heat-affected zones (HAZs) and the user-specified single-laser scanning area are considered. The optimization model is solved by deep reinforcement learning (DRL), offering the flexibility to include or exclude considerations for different quality/process requirements. Two case studies demonstrate the application of DRL models considering different sets of constraints and compare their performance with two baseline scheduling methods in terms of fabrication efficiency and violation of quality constraints. In addition, the impact of the laser number on operational improvement and the computational cost of the DRL model is also studied.