We report a study of the electron–phonon contribution to the linewidth of quantum-well states in a surface superstructure formed by a 4/3-monolayer of Pb on Si(111), a dense phase with a 3×3 unit cell. Ab initio calculations based on the density-functional theory were carried out using a linear response approach in the mixed-basis pseudopotential representation. The phonon-induced contribution to the lifetime broadening is analyzed for both excited electrons and holes. The phonon contribution is found to be generally very sensitive to the energy position of the excited electron (hole) except for unoccupied Pb electronic states inside the Si band gap where the phonon-induced linewidth varies smoothly around ∼ 13 meV irrespective of electron energy. This differs for occupied Pb electronic states, which exhibit larger linewidths, or shorter lifetimes, because numerous phonon-mediated transitions to Si electronic bands substantially increase the electron–phonon coupling.