The correct statements are I. The low solubility of LiF is due to its high lattice enthalpy. II. LiBr is not soluble in acetone. III. LiCl is soluble in pyridine. IV. The order of melting points of alkali metal halides is $M F>M C l>M B r>M I$.

$\mathrm{Li}^{+}$has high hydration enthalpy but it has high lattice enthalpy in LiF. The lattice enthalpy is higher than hydration enthalpy resulting into low solubility. LiCl is covalent due to small size of cation and large size of anion. So, it is non-polar and due to better solute-solvent interaction, $\mathrm{LiCl}$ is soluble in pyridine. In alkali metal halides, the melting point decreases with increase in covalent character which increases with the size of anion in ionic compound. So, the order of melting point is $$ M F>M C l>M B r>M I $$ Hence, the correct statements are I, III and IV.