The transient dynamic response of a bridge crane’s lifting mechanism is critical for operational safety and structural fatigue life. While traditional multi-body dynamics simulations offer high fidelity, their substantial computational cost hinders real-time analysis in digital twin applications. To overcome this bottleneck, this paper proposes a deep learning surrogate model based on a Long Short-Term Memory (LSTM) network for rapid prediction of the transient dynamics in a double-girder bridge crane’s lifting system. First, a high-fidelity dynamic benchmark model incorporating wire rope flexibility and contact friction is developed in ADAMS. Second, a high-quality dataset of 400 samples is constructed via Latin Hypercube Sampling, covering variations in load, lifting height, speed, and acceleration. Third, a three-layer encoder-LSTM-decoder network is designed and trained using a cosine annealing learning rate schedule and the AdamW optimizer. Experimental results demonstrate that the proposed model achieves excellent prediction accuracy, with a normalized mean absolute error (NMAE) of 0.0431, a normalized root mean square error (NRMSE) of 0.0681, and an average peak relative error of 4.72%, meeting engineering requirements. Most notably, the prediction time is reduced from approximately 30 minutes per simulation to 300 milliseconds, representing a computational efficiency improvement by a factor of about 6000 compared to conventional dynamic simulation.