In this paper, a neural network-based Lyapunov approach is proposed to evaluate the closed-loop control stability of an accurately simulated model of an unmanned aerial vehicle. The neural controller is trained offline based on an optimal LQR controller, while another network is enabled to generate a Lyapunov function for the entire closed-loop system. The benefits of the approach, including real-time performance and a more energy-efficient realization of the controller, are highlighted with respect to a number of applications, including hovering, even in the presence of wind disturbances and generalization to trajectory tracking.