Neutron resonance spin-echo spectroscopy was used to monitor the temperature evolution of the linewidths of transverse acoustic phonons in lead across the superconducting transition temperature over an extended range of the Brillouin zone. For phonons with energies below the superconducting energy gap, a linewidth reduction of maximum amplitude was observed below . The electron-phonon contribution to the phonon lifetime extracted from these data is in satisfactory overall agreement with ab initio lattice-dynamical calculations, but significant deviations are found.