Insolubility of LiF in water can be elucidated as follows:
The lithium ion has the highest energy of hydration as it is small in size in comparison to the other alkali metal ions and so it should be highly soluble. But the small Li+ and F– ions interact very strongly resulting in high lattice energy of LiF which is responsible for its insolubility whereas in LiCl due to the difference in atomic size between Li+ and Cl–, they do not interact very strongly, the lattice energy is comparatively small and the magnitude of hydration enthalpy is quite large. Therefore, LiCl dissolves in water. As LiCl has more covalent character than LiF (Fajan’s rule) thus, it is soluble in organic solvents like acetone.