Due to their flexibility and low cost deployment, unmanned aerial vehicles (UAV) will most likely act as base stations and backhaul relays in the next generation of wireless communication systems. However, these UAVs—in the untethered mode—can only operate for a finite time due to limited energy they carry in their batteries. In free-space optical communications, one solution is to transport both the data and the energy from the source to the UAV through the laser beam—a concept known as simultaneous lightwave information and power transfer (SLIPT). In this study, we have analyzed the SLIPT scheme for laser-powered decode-and-forward UAV relays in an optical wireless backhaul. The major goal of this study is to optimally allocate the received beam energy between the decoding circuit, the transmitting circuit and the rotor block of the relay in order to maximize a quality-of-service metric such as maximum achievable rate, outage or error probabilities. As expected, we note that the optimal power allocation depends heavily on the source-relay and relay-destination channel conditions. In the final part of this study, we have maximized the operational time of the UAV relay given that the maximum achievable rate stays above a certain threshold in order to meet a minimum quality-of-service requirement.