The lungs of squamate reptiles (lizards and snakes) are highly diverse, exhibiting single chambers, multiple chambers, transitional forms with two to three chambers, along with a suite of other anatomical features, including finger-like epithelial projections into the body cavity known as diverticulae. During embryonic development of the simple, sac-like lungs of anoles, the epithelium is pushed through the openings of a pulmonary smooth muscle mesh by the forces of luminal fluid pressure. This process of stress ball morphogenesis generates the faveolar epithelium typical of squamate lungs. Here, we compared embryonic lung development in brown anoles, leopard geckos, and veiled chameleons to determine if stress ball morphogenesis is conserved across squamates and to understand the physical processes that generate transitional-chambered lungs with diverticulae. We found that epithelial protrusion through the holes in a pulmonary smooth muscle mesh is conserved across squamates. Surprisingly, however, we found that luminal inflation is not conserved. Instead, leopard geckos and veiled chameleons appear to generate their faveolae via epithelial folding downstream of epithelial proliferation. We also found experimental and computational evidence suggesting that the transitional chambers and diverticulae of veiled chameleon lungs develop via apical constriction, a process known to be crucial for airway branching in the bird lung. Thus, distinct morphogenetic mechanisms generate epithelial diversity in squamate lungs, which may underpin their species-specific physiological and ecological adaptations.