As a fundamental data format representing spatial information, depth map is widely used in signal processing and computer vision fields. Massive amount of high precision depth maps are produced with the rapid development of equipment like laser scanner or LiDAR. Therefore, it is urgent to explore a new compression method with better compression ratio for high precision depth maps. Utilizing the wide spread deep learning environment, we propose an end-to-end learning-based lossless compression method for high precision depth maps. The whole process is comprised of two sub-processes, named pre-processing of depth maps and deep lossless compression of processed depth maps. The deep lossless compression network consists of two sub-networks, named lossy compression network and lossless compression network. We leverage the concept of pseudo-residual to guide the generation of distribution for residual and avoid introducing context models. Our end-to-end lossless compression network achieves competitive performance over engineered codecs and has low computational cost.