Current LiDAR systems are limited in their ability to capture dense 3D point clouds. To overcome this challenge, deep learning-based depth completion algorithms have been developed to inpaint missing depth guided by an RGB image. However, these methods fail for low sampling rates. Here, we propose an adaptive sampling scheme for LiDAR systems that demonstrates state-of-the-art performance for depth completion at low sampling rates. Our system is fully differentiable, allowing the sparse depth sampling and the depth inpainting components to be trained end-to-end with an upstream task.