Lattice models are a common abstraction used in the study of protein structure, folding, and refinement. They are advantageous because the discretisation of space can make extensive protein evaluations computationally feasible. Various approaches to the protein chain lattice fitting problem have been suggested but only a single backbone-only tool is available currently. We introduce LatFit, a new tool to produce high-accuracy lattice protein models. It generates both backbone-only and backbone-side-chain models in any user defined lattice. LatFit implements a new distance RMSD-optimisation fitting procedure in addition to the known coordinate RMSD method. We tested LatFit's accuracy and speed using a large nonredundant set of high resolution proteins (SCOP database) on three commonly used lattices: 3D cubic, face-centred cubic, and knight's walk. Fitting speed compared favourably to other methods and both backbone-only and backbone-side-chain models show low deviation from the original data (~1.5 Å RMSD in the FCC lattice). To our knowledge this represents the first comprehensive study of lattice quality for on-lattice protein models including side chains while LatFit is the only available tool for such models.