Evolutionary radiations into novel areas or niches require innovative adaptations. However, rapid subsequent changes in these novel conditions might demand rapid re-adaptations to secure population persistence and prevent extinction. We propose that reptilian viviparity (live birth) is consistent with such a scenario. Using the Liolaemus lizard radiation, we investigate the hypotheses that historical invasions of cold climates have been permitted by transitions to viviparity, and that this parity mode is irreversible. Then, we investigate whether these combined factors restrict viviparous lizards to cold climates, and hence, whether viviparous species are particularly threatened by climate change.