The function of the lung is closely coupled to its structural anatomy, which varies greatly across vertebrates. Although architecturally simple, a complex pattern of airflow is thought to be achieved in the lizard lung due to its cavernous central lumen and honeycomb-shaped wall. We find that the wall of the lizard lung is generated from an initially smooth epithelial sheet, which is pushed through holes in a hexagonal smooth muscle meshwork by forces from fluid pressure, similar to a stress ball. Combining transcriptomics with time-lapse imaging reveals that the hexagonal meshwork self-assembles in response to circumferential and axial stresses downstream of pressure. A computational model predicts the pressure-driven changes in epithelial topology, which we probe using optogenetically driven contraction of 3D-printed engineered muscle. These results reveal the physical principles used to sculpt the unusual architecture of the lizard lung, which could be exploited as a novel strategy to engineer tissues.