To address the issue of spatiotemporal coupling in random charging loads caused by the large-scale integration of electric vehicles, which disrupts the dynamic stability of microgrids, a Lyapunov-based microgrid optimization scheduling method (LOSM) is proposed. The key innovation lies in its dual virtual queue system, which meticulously models the spatiotemporally coupled randomness of BSS operation without relying on any forecasting, setting it apart from traditional prediction-dependent approaches. First, an energy storage system model incorporating a dynamic energy management mechanism is established. In contrast to traditional forecasting-dependent methods, our approach introduces a virtual queue for the battery unit state of charge (SOC), which enables real-time adaptability and significantly reduces reliance on prediction accuracy. This mechanism accurately characterizes the time-varying charging and discharging processes, thereby mitigating the impact of power fluctuations caused by charging on system frequency stability. Subsequently, a spatiotemporally correlated virtual queue is constructed for the multimodal operation of the battery swapping station, further enhancing real-time tracking capability without requiring high-accuracy forecasts. This achieves multidimensional and precise tracking of its electrical energy state. By integrating these virtual queues with a penalty factor adjustment mechanism, the proposed method simultaneously optimizes operational economy and dynamic stability while satisfying system stability constraints. Simulation analysis under a typical diurnal residential load profile with a 50-EV battery swapping station and a significant penetration of wind and photovoltaic generation demonstrates that the proposed approach increases the revenue of the battery swapping station by 5.67% and reduces the start-stop frequency of the diesel generator by 37.04%. This study provides a theoretical foundation for the robust operation of microgrids in scenarios involving electric vehicle integration and serves as an important reference for establishing dynamic stability assurance mechanisms in new power systems.