Question

LiI is more soluble than KI in ethanol

Answer 1

LiI has a covalent character because Li ion has high polarizing power due to its small size. Therefore LiI is soluble in alcohol. On the other  hand KI is predominantly an ionic compound, therefore is insoluble in ethanol.

Answer 2

Ethanol is a non-polar solvent, therefore, covalent molecules are more soluble in ethanol compare to ionic compounds.  

According to Fajan's rule, a small cation, large anion, and more charge on ion cause polarization of ions that induces the covalent nature in the molecule. Whereas compounds with large cation, small anion, and less charges will make the molecule ionic.

Lithium is the 1st element of 1st group in the periodic table. As we move down in the group, the atomic radii also increases. Hence, due to small size of $Li^+$ ion, it makes covalent compound. Therefore, LiI is a covalent molecule that makes it soluble in ethanol.