LiDAR point clouds are fundamental to various applications, yet high-precision scans incur substantial storage and transmission overhead. Existing methods typically convert unordered points into hierarchical octree or voxel structures for dense-to-sparse predictive coding. However, the extreme sparsity of geometric details hinders efficient context modeling, thereby limiting their compression performance and speed. To address this challenge, we propose to generate compact features for efficient predictive coding. Our framework comprises two lightweight modules. First, the Geometry Re-Densification Module re-densifies encoded sparse geometry, extracts features at denser scale, and then re-sparsifies the features for predictive coding. This module avoids costly computation on highly sparse details while maintaining a lightweight prediction head. Second, the Cross-scale Feature Propagation Module leverages occupancy cues from multiple resolution levels to guide hierarchical feature propagation. This design facilitates information sharing across scales, thereby reducing redundant feature extraction and providing enriched features for the Geometry Re-Densification Module. By integrating these two modules, our method yields a compact feature representation that provides efficient context modeling and accelerates the coding process. Experiments on the KITTI dataset demonstrate state-of-the-art compression ratios and real-time performance, achieving 26 FPS for encoding/decoding at 12-bit quantization. Code is available at https://github.com/pengpeng-yu/FastPCC.