  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, $T_c$, over an extended range of the
Brillouin zone. For phonons with energies below the superconducting energy gap,
a linewidth reduction of maximum amplitude $\sim 6 \mu$eV was observed below
$T_c$. The electron-phonon contribution to the phonon lifetime extracted from
these data is in satisfactory overall agreement with {\it ab-initio}
lattice-dynamical calculations, but significant deviations are found.
