We present LoR-LUT, a unified low-rank formulation for compact and interpretable 3D lookup table (LUT) generation. Unlike conventional 3D-LUT-based techniques that rely on fusion of basis LUTs, which are usually dense tensors, our unified approach extends the current framework by jointly using residual corrections, which are in fact low-rank tensors, together with a set of basis LUTs. The approach described here improves the existing perceptual quality of an image, which is primarily due to the technique's novel use of residual corrections. At the same time, we achieve the same level of trilinear interpolation complexity, using a significantly smaller number of network, residual corrections, and LUT parameters. The experimental results obtained from LoR-LUT, which is trained on the MIT-Adobe FiveK dataset, reproduce expert-level retouching characteristics with high perceptual fidelity and a sub-megabyte model size. Furthermore, we introduce an interactive visualization tool, termed LoR-LUT Viewer, which transforms an input image into the LUT-adjusted output image, via a number of slidebars that control different parameters. The tool provides an effective way to enhance interpretability and user confidence in the visual results. Overall, our proposed formulation offers a compact, interpretable, and efficient direction for future LUT-based image enhancement and style transfer.