As a heavy analog of graphene, plumbene is a two-dimensional material with strong spin-orbit coupling effects. Using scanning tunneling microscopy, we observe that Pb forms a flat honeycomb lattice on an Fe monolayer on Ir(111). In contrast, without the Fe layer, a c(2×4) structure of Pb on Ir(111) is found. We use density-functional theory calculations to rationalize these findings and analyze the impact of the hybridization on the plumbene band structure. In the unoccupied states the splitting of the Dirac cone by spin-orbit interaction is clearly observed, while the occupied Pb states are strongly hybridized with the substrate. In a freestanding plumbene we find a band inversion below the Fermi level that leads to the formation of a topologically nontrivial gap. Exchange splitting as mediated by the strong hybridization with the Fe layer drives a quantum spin Hall to quantum anomalous Hall state transition.