Lattice energy:
The amount of energy required to convert one mole of an ionic solid into gaseous ionic constituents
Or
The amount of energy released when one mole of ionic solid is formed from its gaseous ionic constituents.
Hydration energy
Hydration energy is an amount of energy which is released on hydration of one mole ions. When the solvent is not water it is known as a solvation energy.
Condition for a substance to become soluble
The solubility of a compound in water depends on the balance between lattice energy and hydration energy. When hydration energy of any ion overcomes the amount of lattice energy the bond dissociates, and solubility occurs.
Explanation for the solubility of LiCl and insolubility of LiF
Since fluoride ion is much smaller in size than chloride ion, the lattice energy of LiF is greater than its hydration energy. For LiCl, its hydration energy is more than its lattice energy so it is soluble in water.
Moreover LiCl has partial covalent and partial ionic character due to the polarization of Chloride ion by Lithium ion. So, LiCl is soluble in organic polar solvent also like Acetone.
Very high lattice energy for LiF, it becomes almost insoluble. Partial covalent character and low lattice energy makes LiCl soluble in Water and Acetone
Therefore, LiF is insoluble in water, whereas LiCl is soluble not only in water, but also in acetone.