In this paper, we investigate the uplink transmissions in low-power wide-area networks (LPWAN) where the users are self-powered by the energy harvested from the ambient environment. Demonstrating their potential in supporting diverse Internet-of-Things (IoT) applications, we focus on long range (LoRa) networks where the LoRa users are using the harvested energy to transmit data to a gateway via different spreading codes. Precisely, we study the throughput fairness optimization problem for LoRa users by jointly optimizing the spreading factor (SF) assignment, energy harvesting (EH) time duration, and the transmit power of LoRa users. First, through examination of the various permutations of collisions among users, we derive a general expression of the packet collision time between LoRa users, which depends on the SFs and EH duration requirements. Then, after reviewing prior SF allocation work, we develop two types of algorithms that either assure fair SF assignment indeed purposefully `unfair' allocation schemes for the LoRa users. Our results unearth three new findings. Firstly, we demonstrate that, to maximize the minimum rate, the unfair SF allocation algorithm outperforms the other approaches. Secondly, considering the derived expression of packet collision between simultaneous users, we are now able to improve the performance of the minimum rate of LoRa users and show that it is protected from inter-SF interference which occurs between users with different SFs. That is, imperfect SF orthogonality has no impact on minimum rate performance. Finally, we have observed that co-SF interference is the main limitation in the throughput performance, and not the energy scarcity.