We propose to measure the incoherent neutron spectra of lithium amide (LiNH_2) and imide (Li_2NH) at low temperature (T<20 K). These two substances belong to the Li-H-N system, which has been recently considered for on-board hydrogen storage applications. However, while the the room-temperature crystal structure of the former compound is well established, that of the latter is still highly controversial, with at least six options fully or partially compatible with the diffraction experimental findings (both x-ray and neutron). Given our experience with other ionic hydrides, we believe that incoherent neutron spectra could provide unique information on the proton vibrational dynamics and so they could complement the aforementioned diffraction data, helping (together with appropriate DFT simulations) to shed more light on the elusive lithium imide crystal structure.