Many computational photography applications can be framed as low-dimensional regression problems that require fast evaluation of test samples for rendering. In such cases, storing samples on a grid or lattice that can be quickly interpolated is often a practical approach. We show how to optimally solve for such a lattice given non-lattice data points. The resulting lattice regression is fast and accurate. We demonstrate its usefulness for two applications: color management, and superresolution of omnidirectional images.