In the context of Intelligent Transportation Systems (ITS), efficient data compression is crucial for managing large-scale point cloud data acquired by roadside LiDAR sensors. The demand for efficient storage, streaming, and real-time object detection capabilities for point cloud data is substantial. This work introduces PointCompress3D, a novel point cloud compression framework tailored specifically for roadside LiDARs. Our framework addresses the challenges of compressing high-resolution point clouds while maintaining accuracy and compatibility with roadside LiDAR sensors. We adapt, extend, integrate, and evaluate three cutting-edge compression methods using our real-world-based TUMTraf dataset family. We achieve a frame rate of 10 FPS while keeping compression sizes below 105 Kb, a reduction of 50 times, and maintaining object detection performance on par with the original data. In extensive experiments and ablation studies, we finally achieved a PSNR d2 of 94.46 and a BPP of 6.54 on our dataset. Future work includes the deployment on the live system. The code is available on our project website: https://pointcompress3d.github.io.