Long-range frequency hopping spread spectrum (LR-FHSS) is a pivotal advancement in the LoRaWAN protocol that is designed to enhance the network's capacity and robustness, particularly in densely populated environments. Although energy consumption is paramount in LoRaWAN-based end devices, this is the first study in the literature, to our knowledge, that models the impact of this novel mechanism on energy consumption. In this article, we provide a comprehensive energy consumption analytical model of LR-FHSS, focusing on three critical metrics: average current consumption, battery lifetime, and energy efficiency of data transmission. The model is based on measurements performed on real hardware in a fully operational LR-FHSS network. While in our evaluation, LR-FHSS can show worse consumption figures than LoRa, we find that with optimal configuration, the battery lifetime of LR-FHSS end devices can reach 2.5 years for a 50 min notification period. For the most energy-efficient payload size, this lifespan can be extended to a theoretical maximum of up to 16 years with a one-day notification interval using a cell-coin battery.