A system-optimized framework is presented for learning a multi-dimensional look-up-table (LUT) from training samples. The technique, termed lattice regression, solves for an entire LUT at once by optimizing the three-fold objective of 1) low interpolation error on training data, 2) smooth transitions between adjacent LUT outputs, and 3) a steady overall functional trend. The proposed algorithm is tested for both smoothness and accuracy against state-of-the-art for color management in printers.