Octree-based context learning has recently become a leading method in point cloud compression. However, its potential on lossy compression remains undiscovered. The traditional lossy compression paradigm using lossless octree representation with quantization step adjustment may result in severe distortions due to massive missing points in quantization. Therefore, we analyze data characteristics of different point clouds and propose lossy approaches specifically. For object point clouds that suffer from quantization step adjustment, we propose a new leaf nodes lossy compression method, which achieves lossy compression by performing bit-wise coding and binary prediction on leaf nodes. For LiDAR point clouds, we explore variable rate approaches and propose a simple but effective rate control method. Experimental results demonstrate that the proposed leaf nodes lossy compression method significantly outperforms the previous octree-based method on object point clouds, and the proposed rate control method achieves about 1% bit error without finetuning on LiDAR point clouds.