Li_2NH has been recently considered for H_2 storage applications. However, its low-T crystal structure is still controversial, with at least 6 options compatible with the diffraction findings. Few months ago we have performed IINS measurements on Li_2NH in order to provide complementary information on the H vibrational dynamics and to shed more light (together with appropriate ab-initio simulations) on the elusive Li_2NH structure. Our data analysis has pointed out large differences in the H-projected phonon densities states derived from forward and back-scattering TOSCA detectors. This anomaly has been interpreted as a clear effect of a fast H jump diffusion behaviour, smearing out the lattice vibrational excitations in an angle-dependent way. For this reason, we propose to measure the quasi-elastic neutron spectra of Li_2NH in its low T phase at 9 different temperatures (4 K<T<300 K).