Spatial responses of species to past climate change depend on both intrinsic traits (climatic niche breadth, dispersal rates) and the scale of climatic fluctuations across the landscape. New capabilities in generating and analysing population genomic data, along with spatial modelling, have unleashed our capacity to infer how past climate changes have shaped populations, and by extension, complex communities. Combining these approaches, we uncover lineage diversity across four co-distributed lizards from the Australian Monsoonal Tropics and explore how varying climatic tolerances interact with regional climate history to generate common versus disparate responses to late Pleistocene change. We find more divergent spatial structuring and temporal demographic responses in the drier Kimberley region compared to the more mesic and consistently suitable Top End. We hypothesize that, in general, the effects of species’ traits on sensitivity to climate fluctuation will be more evident in climatically marginal regions. If true, this points to the need in climatically marginal areas to craft more species- (or trait-) specific strategies for persistence under future climate change.