We report on the vibrational dynamics of ${\mathrm{H}}^{\ensuremath{-}}$ local modes in ${\mathrm{LaF}}_{3},{\mathrm{CeF}}_{3},{\mathrm{PrF}}_{3}$, and ${\mathrm{NdF}}_{3}$ crystals, excited using the picosecond infrared output of a free-electron laser. Using a pump-probe technique, the 10 K lifetimes of the $Z$ mode of the principal ${\mathrm{H}}^{\ensuremath{-}}$ centre were measured as $49\ifmmode\pm\else\textpm\fi{}2$, $23\ifmmode\pm\else\textpm\fi{}1$, $16\ifmmode\pm\else\textpm\fi{}1$, and $109\ifmmode\pm\else\textpm\fi{}6\phantom{\rule{0.3em}{0ex}}\mathrm{ps}$ for ${\mathrm{LaF}}_{3},\phantom{\rule{0.3em}{0ex}}{\mathrm{CeF}}_{3},\phantom{\rule{0.3em}{0ex}}{\mathrm{PrF}}_{3}$, and ${\mathrm{NdF}}_{3}$ respectively. Anharmonic decay to two or three lattice-band modes determines these 10 K lifetimes. For ${\mathrm{LaF}}_{3},\phantom{\rule{0.3em}{0ex}}{\mathrm{CeF}}_{3}$, and ${\mathrm{NdF}}_{3}$, these lifetimes decrease with increasing temperature, with inclusion of one-phonon absorption to the higher-lying $(X,Y)$ modes needed to account for the dependence. ${\mathrm{PrF}}_{3}$ is a striking exception to the others in showing an increased lifetime with increasing temperature, with its lifetime increasing from its 10 K value. From a combination of lifetime and infrared linewidth measurements, pure dephasing rates have been derived and these are well accounted for by band-phonon scattering. The $Z$ modes themselves exhibit an anharmonic shift of their line position to lower energies with increasing temperature. Photon-echo techniques have been used to determine the homogeneous linewidths of the ${\mathrm{H}}^{\ensuremath{-}}$ modes and these are in good agreement with 10 K infrared absorption linewidths measured for weakly hydrogenated crystals.