Efficient firmware distributions in energy-harvesting (EH) LoRa networks require that EH LoRa sensors simultaneously receive data fragments from a server without facing power failures. This requirement is difficult to satisfy due to the impact of EH rates and LoRa transmission parameters on the efficiency of firmware distributions. We present FioRa+, a novel energy neutrality-aware multicast firmware distribution framework for EH LoRa networks. It gradually distributes a firmware image to EH LoRa sensors in an energy-neutral manner according to their future energy availability predicted using embedded machine learning models. Consequently, the need for additional firmware distributions caused by unsuccessful firmware image reconstructions is reduced. Through one-hop neighbor discovery, on-demand relay, flexible energy query, and coverage assessment mechanisms, FioRa+ ensures that all EH LoRa sensors can receive data fragments from the server at the scheduled time using high data rates. Equipped with a relay scheduling algorithm, it circumvents the collision of data fragments relayed by EH LoRa sensors using identical data rates. The experimental results show that FioRa+ renders up to 113 × shorter distribution time and 22.7 × less distribution overhead than the state of the art.