In the era of widespread Lithium-ion Battery (LIB) usage, precise prediction of battery Remaining Useful Life (RUL) and recycling nodes is increasingly crucial. This study introduces a hybrid approach, amalgamating Ensemble Empirical Mode Decomposition (EEMD), Light Gradient Boosting Machine (LightGBM), Sliding Window Algorithm (SLA), and Long Short-Term Memory (LSTM) for RUL prediction. EEMD isolates high- and low-frequency parts of the capacity signal. Subsequently, LSTM combined with SLA was used to model the low-frequency portion that reflects the trend of capacity decline. Then set different prediction starting points(SPs) for high-frequency signals and input them into the LSTM network to obtain preliminary prediction results. Reconstruct this result into a new feature matrix and input it into LightGBM to predict the high-frequency part that reflects capacity regeneration. Finally, the prediction results of hybrid model are combined to achieve RUL prediction. The hybrid method achieves less than a 2-cycle error in RUL prediction, with the RMSE (Root Mean Square Error) indicator not exceeding 2.5%, and the MAE (Mean Absolute Error) indicator reaching a minimum of 0.9%. Even when predicting ahead to 80 cycles, the method still maintains an RMSE error below 2.0% and an MAE error of 1.6%. Simultaneously, this method specifically demonstrates predictive capabilities for the capacity regeneration phenomenon. The algorithm, through the integration of mixed artificial intelligence methods, expands the scope of RUL prediction.