NCS is a natural method to investigate nuclear quantum effects in condensed-matter systems and molecules. However, it is not often used as a first method of choice due to the relatively poor visibility of non-Gaussian components in the momentum distribution. To overcome these difficulties, we propose VESUVIO measurements on LiH and LiD at 10K beyond the single-scattering regime using Monte-Carlo fitting techniques. Our methodology to obtain atomic-momentum distributions from first-principles calculations (recently tested on LiH and LiD) will be used to compare these experimental data with ab initio results. Use of a generalized non-Gaussian model as a seed for a MC transport-code calculation will enable to fit both single- and multiple-scattering contributions and provide fresh insights into the effective local Born-Oppenheimer potential in LiH/LiD.