Lithium-beryllium metal hydrides, which are structurally related to their parent compound, BeH₂, offer the highest hydrogen storage capacity by weight among the metal hydrides (15.93 wt. % of hydrogen for LiBeH₃). Challenging synthesis protocols have precluded conclusive determination of their crystallographic structure to date, but here we analyze directly the hydrogen hopping mechanisms in BeH₂ and LiBeH₃ using quasielastic neutron scattering, which is especially sensitive to single-particle dynamics of hydrogen. We find that, unlike its parent compound BeH₂, lithium-beryllium hydride LiBeH₃ exhibits a sharp increase in hydrogen mobility above 265 K, so dramatic that it can be viewed as melting of hydrogen sublattice. We perform comparative analysis of hydrogen jump mechanisms observed in BeH₂ and LiBeH₃ over a broad temperature range. As microscopic diffusivity of hydrogen is directly related to its macroscopic kinetics, a transition in LiBeH₃ so close to ambient temperature may offer a straightforward and effective mechanism to influence hydrogen uptake and release in this very lightweight hydrogen storage compound.