In the current work, we study inorganic solid-state electrolytes for lithium-ion batteries. These materials, unlike the traditional 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 MuonSR experiments on a series of LiAlX4 (X = Cl, Br, I) samples. Our interest is to asses the effect of both the mechanochemical synthesis and the varying polarizability of the anion framework (as a function of X). In order to obtain a definitive model of the crystal structure, we will also perform PND studies. These complementary studies will be of key importance to propose valid conduction mechanisms in our materials.