This is the data package for the publication with the above title. The data and python scripts to reproduce the figures in the manuscript and supplementary information is provided in the folder "Data". In the folder "Code", we provide all the C++ codes used for the bacterial colony simulations and the fluid simulations. Each folder contains a readme.txt that describes what the files are, and how to compile and run the various codes. Using the simulation code, discrete orientational symmetries in hybrid lattice-based models of bacterial colony growth was investigated on square and disordered lattices. Three different disordered lattices were studied: two disordered lattices derived from a square reference lattice as proposed in literature and a fluid-derived lattice. The included fluid simulation code was used to generate the fluid-derived lattice. After generating a set of pseudo-random points, the lattice was constructed by applying a Voronoi tessellation. The Voro++ software package was used to compute this tessellation. The presence of discrete orientational symmetries in colony shapes was assessed by fitting convex hulls to the colonies. All three disordered lattices were able to reduce the observed discrete symmetry. However, only the fluid-derived lattice was able to resolve this artefact in all models investigated.