In the current work, we study inorganic solid-state electrolytes for lithium-ion batteries. These materials, unlike liquid electrolytes, could lead to a breakthrough in battery lifetime and safety, since the use of flammable organic solvents is no longer needed. Our aim is to study the ways in which the ionic conductivity can be tuned and contribute to the understanding of the synthesis-structure-property relationships. We propose to perform INS experiments on a series of LiMX4 (M= Al, Ga; X = Cl, Br, I) samples. Our interest is to asses the effect of both the mechanochemical synthesis and the varying polarisability of the anion framework (as a function of X). In order to explain experimental observations we have also performed phonon calculations by DFT. These complementary studies will be of key importance to propose valid correlations and interpret experimental data.