Background Diet is a key component of a species ecological niche and plays critical roles in guiding the trajectories of evolutionary change. Previous studies suggest that dietary evolution can influence the rates and patterns of species diversification, with omnivorous (animal and plant, 'generalist') diets slowing down diversification compared to more restricted ('specialist') herbivorous and carnivorous diets. This hypothesis, here termed the "dietary macroevolutionary sink" hypothesis (DMS), predicts that transitions to omnivorous diets occur at higher rates than into any specialist diet, and omnivores are expected to have the lowest diversification rates, causing an evolutionary sink into a single type of diet. However, evidence for the DMS hypothesis remains conflicting. Here, we present the first test of the DMS hypothesis in a lineage of ectothermic tetrapods-the prolific Liolaemidae lizard radiation from South America. Results Ancestral reconstructions suggest that the stem ancestor was probably insectivorous. The best supported trait model is a diet-dependent speciation rate, with independent extinction rates. Herbivory has the highest net diversification rate, omnivory ranks second, and insectivory has the lowest. The extinction rate is the same for all three diet types and is much lower than the speciation rates. The highest transition rate was from omnivory to insectivory, and the lowest transition rates were between insectivory and herbivory. Conclusions Our findings challenge the core prediction of the DMS hypothesis that generalist diets represent an 'evolutionary sink'. Interestingly, liolaemid lizards have rapidly and successfully proliferated across some of the world's coldest climates (at high elevations and latitudes), where species have evolved mixed arthropod-plant (omnivore) or predominantly herbivore diets. This longstanding observation is consistent with the higher net diversification rates found in both herbivory and omnivory. Collectively, just like the evolution of viviparity has been regarded as a 'key adaptation' during the liolaemid radiation across cold climates, our findings suggest that transitions from insectivory to herbivory (bridged by omnivory) are likely to have played a role as an additional key adaptation underlying the exceptional diversification of these reptiles across extreme climates.