Airborne radio access networks (A-RANs) is a particularly promising technology due to its ability to offer fast, cost-efficient, and on- demand enhancement of the existing telecommunication infrastructure. The main challenges of ARANs are the energy sustainability of the aerial platforms (APs) and the establishment of reliable links with the ground nodes. To this direction, we propose a novel approach, which is based on mixed free-space optical (FSO)/radio frequency (RF) relaying protocol and simultaneous lightwave information and power transfer (SLIPT). In this context, we also formulate and optimally solve the max-min fairness problem, which regulates the trade-off between the energy and information transfer to the AP and allocates the available resources to multiple end-users. Finally, the impact of the number of users and weather conditions on system's optimal configuration and performance is investigated through simulations. The offered results provide meaningful theoretical and practical insights on the capabilities of the proposed scheme.