Lithium imide (Li2NH) and amide (LiNH2) belong to the Li-H-N system, which has been recently considered for on-board hydrogen storage applications. However the imide low-temperature crystal structure is still highly controversial, with at least six options compatible with the diffraction experimental findings. A complementary study on low-temperature Li2NH and LiNH2 has been recently accomplished by the authors using neutron spectroscopy (with energy transfer in the 3-500 meV range). The rationale of these measurements was that crystal structures (especially their proton arrangements) affect in a strong way the neutron scattering spectra, so that a combined use of computer ab-initio simulations and inelastic neutron scattering could be a stringent validation method for the various models. Data analysis has pointed out broad and almost featureless proton-projected phonon densities of states for lithium imide, with large differences in the data sets derived from forward scattering and backscattering detector banks. On the contrary, a sharp phonon spectrum and much less discrepancy was found applying the same analytic procedure to lithium amide. This Li2NH peculiarity has been interpreted as an effect of the fast proton jump diffusion among the available lattice sites, which smears out the phonon vibrational excitations in a momentum transfer-dependent way.