Many internal organs in multicellular organisms comprise epithelia which enclose fluid-filled cavities referred to as lumens. Lumen formation is regulated by a wide range of processes, including epithelial polarization, secretion, exocytosis and actomyosin contractility. While these mechanisms have shed light on lumen growth, what controls lumen shape remains enigmatic. Here we used pancreas organoids to explore how lumen acquire a spherical shape or a branched topology. Combining computational simulations based on a phase field model and experimental measurements we reveal that the balance between the cell-cycle timing and lumen pressure are critical in regulating lumen morphology. Moreover, we show that by manipulating proliferation and lumen pressurein-silicoandin-vitro, we can alter the morphological trajectories of the lumen during culture growth. Furthermore, we highlighted the crucial role of epithelial permeability, showing that increased permeability led to lower lumen pressure and more complex shapes. Artificially increasing permeability transformed spherical organoids into branching-like structures. In summary, the study underscores the importance of balancing cell proliferation, lumen pressure, and epithelial permeability in determining lumen morphology, providing insights relevant to other organs, for tissue engineering and cystic disease understanding.