Lumen formation in organ epithelia involves processes such as polarization, secretion, exocytosis and contractility, but what controls lumen shape remains unclear. Here we study how lumina develop spherical or complex structures using pancreatic organoids. Combining computational phase-field modelling and experiments, we found that lumen morphology depends on the balance between cell cycle duration and lumen pressure, low pressure and high proliferation produce complex shapes. Manipulating proliferation and lumen pressure can alter or reverse lumen development both in silico and in vitro. Increasing epithelial permeability reduces lumen pressure, converting from spherical to complex lumina. During pancreas development, the epithelium is initially permeable and becomes sealed, experimentally increasing permeability at late stages impairs ductal morphogenesis. Overall, our work underscores how proliferation, pressure and permeability orchestrate lumen shape, offering insights for tissue engineering and cystic disease treatment.