Spin-polarized scanning tunneling microscopy reveals that the spin-spiral period of a two-atomic-layer-thick Fe film on Ir(111) roughly doubles upon covering the system with a monolayer of Pb. The spin spirals have a zigzag shape and are guided by structural dislocation lines. In contrast to the spin spiral in the bare Fe double layer, the magnetic state of the Pb-covered Fe film responds to an external magnetic field: the spin spiral breaks up into segments, reminiscent of the spin-spiral state in the Fe triple layer on Ir(111), where the external magnetic field induces magnetic skyrmions. This demonstrates that the tuning of noncollinear spin textures is not only possible by interface engineering based on transition metals, but also with other metallic adlayers such as Pb with a filled d shell.