The deployment of humanoid robots for dexterous manipulation in unstructured environments remains challenging due to perceptual limitations that constrain the effective workspace. In scenarios where physical constraints prevent the robot from repositioning itself, maintaining omnidirectional awareness becomes far more critical than color or semantic information.While recent advances in visuomotor policy learning have improved manipulation capabilities, conventional RGB-D solutions suffer from narrow fields of view (FOV) and self-occlusion, requiring frequent base movements that introduce motion uncertainty and safety risks. Existing approaches to expanding perception, including active vision systems and third-view cameras, introduce mechanical complexity, calibration dependencies, and latency that hinder reliable real-time performance. In this work, We propose OmniDP, an end-to-end LiDAR-driven 3D visuomotor policy that enables robust manipulation in large workspaces. Our method processes panoramic point clouds through a Time-Aware Attention Pooling mechanism, efficiently encoding sparse 3D data while capturing temporal dependencies. This 360° perception allows the robot to interact with objects across wide areas without frequent repositioning. To support policy learning, we develop a whole-body teleoperation system for efficient data collection on full-body coordination. Extensive experiments in simulation and real-world environments show that OmniDP achieves robust performance in large-workspace and cluttered scenarios, outperforming baselines that rely on egocentric depth cameras.