The dynamic structure functionS(k,?)informs about the dispersion and damp-ing of excitations. We have recently (Beauvois et al. in Phys Rev B 97:184520,2018) compared experimental results forS(k,?)from high-precision neutron scat-tering experiments and theoretical results using the ?dynamic many-body theory?(DMBT), showing excellent agreement over the whole experimentally accessible pres-sure regime. This paper focuses on the specific aspect of the propagation of low-energyphonons. We report calculations of the phonon mean-free path and phonon lifetimein liquid4He as a function of wavelength and pressure. Historically, the question wasof interest for experiments of quantum evaporation. More recently, there is interest inthe potential use of4He as a detector for low-energy dark matter (Schulz and Zurekin Phys Rev Lett 117:121302/1,2016). While the mean-free path of long wavelengthphonons is large, phonons of intermediate energy can have a short mean-free path ofthe order of?m. Comparison of different levels of theory indicates that reliable pre-dictions of the phonon mean-free path can be made only by using the most advancedmany-body method available, namely DMBT.