Since the data volume of LiDAR point clouds is very huge, efficient compression is necessary to reduce their storage and transmission costs. However, existing learning-based compression methods do not exploit the inherent angular resolution of LiDAR and ignore the significant differences in the correlation of geometry information at different bitrates. The predictive geometry coding method in the geometry-based point cloud compression (G-PCC) standard uses the inherent angular resolution to predict the azimuth angles. However, it only models a simple linear relationship between the azimuth angles of neighboring points. Moreover, it does not optimize the quantization parameters for residuals on each coordinate axis in the spherical coordinate system. We propose a learning-based predictive coding method (LPCM) with both high-bitrate and low-bitrate coding modes. LPCM converts point clouds into predictive trees using the spherical coordinate system. In high-bitrate coding mode, we use a lightweight Long-Short-Term Memory-based predictive (LSTM-P) module that captures long-term geometry correlations between different coordinates to efficiently predict and compress the elevation angles. In low-bitrate coding mode, where geometry correlation degrades, we introduce a variational radius compression (VRC) module to directly compress the point radii. Then, we analyze why the quantization of spherical coordinates differs from that of Cartesian coordinates and propose a differential evolution (DE)-based quantization parameter selection method, which improves rate-distortion performance without increasing coding time. Experimental results on the LiDAR benchmark \textit{SemanticKITTI} and the MPEG-specified \textit{Ford} datasets show that LPCM outperforms G-PCC and other learning-based methods.