This paper presents L-Learning, a novel data-driven control framework for robotics that integrates Lyapunov stability theory with Lagrangian mechanics to enhance trajectory tracking performance. While traditional control methods often suffer from performance degradation in dynamic and uncertain environments, data-driven approaches, while more adaptable, are frequently limited by high sample complexity and a lack of rigorous stability guarantees. L-Learning mitigates these challenges by explicitly learning the system's energy function from data, thereby optimizing performance while ensuring closed-loop stability intrinsically. Characterized by superior control accuracy, theoretical stability guarantees, and high sample efficiency, L-Learning represents a promising solution for practical robotic applications.