The datasets contains species presence and background points, and their associated environmental data for non-native common wall lizard (Podarcis muralis). These data are included for local and national scale modelling of likelihood of species presence, as used in the modelling software MaxEnt. The .asc files included are the raw spatial data of parameters (i.e., distance to nearest road) used in modelling at various local regions, from which SWD 'samples with data' were extracted. Outputs from the local MaxEnt models produced the .txt files included. These serve as landscape layer inputs (habitat suitability and movement cost layers) for modelling population growth and spatial spread in the Individual based modelling platform, RangeShifter. Subsequent outputs of projected population growth (number of individuals per landscape cell) and x/y coordinates for each cell, are presented in files with the prefix Pop.csv and avg.csv (averaged data over 50 replicate runs). Full details about this dataset can be found at https://doi.org/10.5285/8ae3f9ef-9a75-4237-afbd-e01abe02e75b