Why is LiF almost insoluble in water whereas LiCl soluble not only in water but also in acetone?

In this case the hydration enthalpy is very less. Hence, LiF is insoluble in water. Due to its low hydration energy and partial covalent and partial ionic character LiCl is soluble in wateras well as acetone.

The low solubiLity of LiF in water is due to its very high Lattice enthalpy (F^- ion is very small in size). On the other hand, in lithium chloride (LiCl) the lattice enthaipy is comparatively very small. This means that the magnitude of hydration enthalpy is quite large. Therefore lithium chloride dissolves in water. It is also soluble in acetone due to dipolar attraction (Acetone is polar in nature).