Cellular organization into epithelial architecture maintains structural integrity and homeostasis by suppressing cell proliferation and apoptosis. However, it is unclear whether the epithelial organization is sufficient to block induction of cell-autonomous cell cycle progression and apoptotic sensitivity by activated oncogenes. We show that chronic activation of oncogenic c-Myc, starting in the developing 3D organotypic mammary acinar structures, results in hyperproliferation and transformed acinar morphology. Surprisingly, acute c-Myc activation in mature quiescent acini with established epithelial architecture fails to reinitiate the cell cycle or transform these structures. c-Myc does reinitiate the cell cycle in quiescent, but structurally unorganized, acini, which demonstrates that proper epithelial architecture is needed for the proliferation blockade. The capability of c-Myc to reinitiate the cell cycle in acinar structures is also restored by the loss of LKB1, a human homologue of the cell polarity protein PAR4. The epithelial architecture also restrains the apoptotic activity of c-Myc, but coactivation of c-Myc and a complementary TNF-related apoptosis-inducing ligand death receptor pathway can induce a strong Bim and Bid-mediated apoptotic response in the established acini. The results together expose surprising proliferation and apoptosis resistance of organized epithelial structures and identify a role for the polarity regulator LKB1 in the development of c–Myc-resistant cell organization.