This paper proposes a continuous-time LSTM neural network as an end-to-end controller for four-wheel steering (4WS) path tracking. Without offline data, reference models, or expert demonstrations, the controller learns online from real-time tracking error and maps lateral and heading error directly to front and rear steering commands. The proposed method is evaluated on a slalom track under combined disturbances including actuator bias, Ornstein-Uhlenbeck colored noise, and a lateral wind gust. Simulation results show that the LSTM weights converge within a few episodes and maintain near-nominal tracking performance under disturbance, whereas a tuned PID baseline exhibits substantially larger RMSE increases. These results suggest that online LSTM adaptation improves robustness for 4WS path tracking under combined disturbances.