Robust radar object classification is a challenging task, primarily due to the aspect sensitivity limitation of one-dimensional High-Resolution Range Profile (HRRP) data. To address this, we propose Point-HRRP-Net. This multi-modal framework integrates HRRP with 3D LiDAR point clouds via a Bi-Directional Cross-Attention (Bi-CA) mechanism to enable deep feature interaction. Since paired real-world data is scarce, we constructed a high-fidelity simulation dataset to validate our approach. Experiments conducted under strict angular separation demonstrated that Point-HRRP-Net consistently outperformed single-modality baselines. Our results also verified the effectiveness of Dynamic Graph CNN (DGCNN) for feature extraction and highlighted the high inference speed and the potential of Mamba- based architectures for future efficient designs. Finally, this work validates the feasibility of the proposed approach in simulated environments, establishing a foundation for robust object classification in real-world scenarios.