Efficient 3D LiDAR point cloud compression (LPCC) and streaming are critical for edge server-assisted robotic systems, enabling real-time communication with compact data representations. A widely adopted approach represents LiDAR point clouds as range images, enabling the direct use of mature image and video compression codecs. However, because these codecs are designed with human visual perception in mind, they often compromise geometric details, which downgrades the performance of downstream robotic tasks such as mapping and object detection. Furthermore, rate-distortion optimization (RDO)-based rate control remains largely underexplored for range image compression (RIC) under dynamic bandwidth conditions. To address these limitations, we propose D-Compress, a new detail-preserving and fast RIC framework tailored for real-time streaming. D-Compress integrates both intra- and inter-frame prediction with an adaptive discrete wavelet transform approach for precise residual compression. Additionally, we introduce a new RDO-based rate control algorithm for RIC through new rate-distortion modeling. Extensive evaluations on various datasets demonstrate the superiority of D-Compress, which outperforms state-of-the-art (SOTA) compression methods in both geometric accuracy and downstream task performance, particularly at compression ratios exceeding 100x, while maintaining real-time execution on resource-constrained hardware. Moreover, evaluations under dynamic bandwidth conditions validate the robustness of its rate control mechanism.