Future missions to the Moon and beyond are likely to involve low-thrust propulsion technologies due to their propellant efficiency. However, these still present a difficult trajectory design problem, owing to the near continuous thrust, lack of control authority and chaotic dynamics. Lyapunov control laws can generate sub-optimal trajectories for such missions with minimal computational cost and are suitable for feasibility studies and as initial guesses for optimisation methods. In this work a Reinforced Lyapunov Controller is used to design optimal low-thrust transfers from geostationary transfer orbit towards lunar polar orbit. Within the reinforcement learning (RL) framework, a dual-actor network setup is used, one in each of the Earth- and Moon-centred inertial frames respectively. A key contribution of this paper is the demonstration of a forwards propagated trajectory, removing the need to define a patch point a priori. This is enabled by an adaptive patch distance and extensive initial geometry exploration during the RL training. Results for both time- and fuel-optimal transfers are presented, along with a Monte Carlo analysis of the robustness to disturbances for such transfers. Phasing is introduced where necessary to aid rendezvous with the Moon. The results demonstrate the potential for such techniques to provide a basis for the design and guidance of low-thrust lunar transfers.