To meet the requirements for managing unauthorized UAVs in the low-altitude economy, a multi-modal UAV trajectory prediction method based on the fusion of LiDAR and millimeter-wave radar information is proposed. A deep fusion network for multi-modal UAV trajectory prediction, termed the Multi-Modal Deep Fusion Framework, is designed. The overall architecture consists of two modality-specific feature extraction networks and a bidirectional cross-attention fusion module, aiming to fully exploit the complementary information of LiDAR and radar point clouds in spatial geometric structure and dynamic reflection characteristics. In the feature extraction stage, the model employs independent but structurally identical feature encoders for LiDAR and radar. After feature extraction, the model enters the Bidirectional Cross-Attention Mechanism stage to achieve information complementarity and semantic alignment between the two modalities. To verify the effectiveness of the proposed model, the MMAUD dataset used in the CVPR 2024 UG2+ UAV Tracking and Pose-Estimation Challenge is adopted as the training and testing dataset. Experimental results show that the proposed multi-modal fusion model significantly improves trajectory prediction accuracy, achieving a 40% improvement compared to the baseline model. In addition, ablation experiments are conducted to demonstrate the effectiveness of different loss functions and post-processing strategies in improving model performance. The proposed model can effectively utilize multi-modal data and provides an efficient solution for unauthorized UAV trajectory prediction in the low-altitude economy.