While advances in wireless networks enable novel services with previously unreachable latency guarantees, edge computing becomes essential for delivering computing resources close to the users and meeting the strict latency requirements. However, addressing the energy footprint of computing resources is crucial amid the pressing sustainability concerns. The energy consumption of idle resources accounts for a significant part of the total energy footprint. While server shutdown during low-demand periods is common in cloud computing, it is challenging to determine which edge servers to shut down and how to route requests due to the stringent latency requirements of the applications. Thus, this work formulates an optimal orchestration policy to minimize the energy consumption of the edge computing infrastructure and presents LESS-ON, a strategy with a polynomial time complexity that reduces the operational energy footprint of edge computing by shutting down edge servers during low-demand periods. In contrast to previous studies, LESS-ON considers the energy requirements associated with routing requests to the designated edge servers. Our numerical evaluation shows that LESS-ON reduces the total consumption by 42% with respect to the common always-on approach during low-demand periods and by 35% over 24 h, all while meeting latency requirements.