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Lidars are depth measuring sensors widely used in autonomous driving and augmented reality. However, the large volume of data produced by lidars can lead to high costs in data storage and transmission. While lidar data can be represented as two interchangeable representations: 3D point clouds and range images, most previous work focus on compressing the generic 3D point clouds. In this work, we show that directly compressing the range images can leverage the lidar scanning pattern, compared to compressing the unprojected point clouds. We propose a novel data-driven range image compression algorithm, named RIDDLE (Range Image Deep DeLta Encoding). At its core is a deep model that predicts the next pixel value in a raster scanning order, based on contextual laser shots from both the current and past scans (represented as a 4D point cloud of spherical coordinates and time). The deltas between predictions and original values can then be compressed by entropy encoding. Evaluated on the Waymo Open Dataset and KITTI, our method demonstrates significant improvement in the compression rate (under the same distortion) compared to widely used point cloud and range image compression algorithms as well as recent deep methods.