In industrial transportation applications, multi-robot systems (MRS) are assigned to perform transportation tasks until their batteries are depleted, requiring them to move to battery charging stations. This temporary unavailability of the robots during charging decreases system productivity that measures the number of transportation tasks accomplished with the available robot energy. As a result, maximizing task completion becomes crucial, especially with prioritized tasks and increased workload. This can be achieved through an energy management strategy. In this context, the Lexicographic Optimization-based Multi-Robot Task Allocation (LO-MRTA) approach is proposed to maximize the reward in terms of system productivity with limited energy consumption. The existing multi-robot energy management approaches consider energy management during the tasks execution and neglect workload scaling issue with increasing tasks, whereas the LO-MRTA approach accounts for the energy consumption in the large-scale tasks allocation process. The main idea of the proposed approach is to consider the global state of the robots in the MRS system before carrying out the tasks execution, enhancing the task allocation decisions in terms of energy management. The evaluation scenarios show the promising performance of the LO-MRTA approach in comparison with three existing baselines in terms of system productivity, overall energy consumption, and workload scaling effects.