Large lakes play an important role in water resource supply, regional climate regulation, and ecosystem support, but they face threats from frequent extreme drought events, necessitating an understanding of the mechanisms behind these events. In this study, we developed an explainable machine learning (ML) model that combines the Bayesian optimized (BO) long short-term memory (LSTM) model and the integrated gradients (IG) interpretation method to simulate and explain lake water level variations. In addition, the hydrological drought trends and extreme drought events in Poyang Lake from 1960 to 2022 were identified using the standardized water level index (SWI) and run theory. The analysis revealed that the frequency of hydrological droughts in Poyang Lake increased from 1960 to 2022, especially in the autumn after 2003. By selecting the flows of the catchment and the Yangtze River as the input features, the BO-LSTM model accurately predicted the water level of Poyang Lake. The IG method was then used to interpret the prediction results from three aspects: the importance ranking of the input features, their roles in the seasonal drought trends, and their roles in extreme drought events. The results indicate that (1) the most influential factor affecting the water level of Poyang Lake was the inflow of the Ganjiang River in the catchment. (2) The increase in the lake outflow caused by the Yangtze River's draining effect was the reason for the intensification of the autumn drought in Poyang Lake. (3) The extreme hydrological drought events were primarily caused by low catchment inflows. Overall, this research provides a new approach that balances prediction accuracy with interpretability for predicting and understanding the hydrological processes in large river-connected lakes. Moreover, this method was also applied to the attribution analysis of hydrological drought in Poyang Lake, providing theoretical support for regional water resource management.