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Prolonging the network lifetime is a major consideration in many Internet of Things applications. In this paper, we study maximizing the network lifetime of an energy-harvesting LoRa network. Such a network is characterized by heterogeneous recharging capabilities across the nodes that is not taken into account in existing work. We propose a link-layer protocol to achieve a long-lived LoRa network which dynamically enables the nodes with depleting batteries to exploit the superfluous energy of the neighboring nodes with affluent batteries by letting a depleting node offload its packets to an affluent node. By exploiting the LoRa's capability of adjusting multiple transmission parameters, we enable low-cost offloading by depleting nodes instead of high-cost direct forwarding. Such offloading requires synchronization of wake-up times as well as transmission parameters between the two nodes which also need to be selected dynamically. The proposed protocol addresses these challenges and prolongs the lifetime of a LoRa network through three novel techniques. (1) We propose a lightweight medium access control protocol for peer-to-peer communication to enable packet offloading which circumvents the synchronization overhead between the two nodes. (2) We propose an intuitive heuristic method for effective parameter selections for different modes (conventional vs. offloading). (3) We analyze the energy overhead of offloading and, based on it, the protocol dynamically selects affluent and depleting nodes while ensuring that an affluent node is not overwhelmed by the depleting ones. Simulations in NS-3 as well as real experiments show that our protocol can increase the network lifetime up to $4$ times while maintaining the same throughput compared to traditional LoRa network.