The dynamic nature of UAV-enabled Mobile Edge Computing (MEC) systems poses significant challenges in balancing latency, energy consumption, and queue stability under fluctuating network conditions. This study proposes a hybrid Lyapunov-Simulated Annealing (Lya-SA) framework to address the real-time adaptability and global-local optimization trade-off in task offloading. By integrating Lyapunov optimization for short-term stability control and Simulated Annealing for global search capability, the framework dynamically adjusts offloading decisions based on queue states and SA temperature decay. Key innovations include the reformulation of the optimization problem into a Lyapunov drift-plus-penalty minimization and the adaptive SA parameter tuning for dynamic environments. Experimental results demonstrate that the proposed method reduces decision latency by 44% compared to local computing and 67% compared to pure edge computing, while maintaining queue stability under varying workloads. This work provides a robust solution for UAV-MEC systems, highlighting the synergy between stability-driven control and metaheuristic optimization in complex scenarios.