Ionic Character, on which factors do it depend
When you are considering lattice energy as the parameter for judging the ionic character of compounds, you are assuming two things.


The constituting elements of this alkali metal halides are purely ionic,and thus the Lattice energy (U) is the released energy when those two isolated gaseous ions forms the crystal lattice. But, in practice the constituting ions are never purely ionic (especially smaller alkali metal halide such as $\ce{LiF} $ or $\ce{NaF}$.)
The ions constituting the crystal lattice are hard non-elastic spheres. They hardly (in general) obey this postulate. This postulate is again not totally valid for smaller alkali metal halides due to distortion of their electron cloud due to large polarization.


So, it is seen that if you just theoretically say that the electrostatic force as simply Coulomb's law and thus lattice energy decreases, it doesn't conclude anything as it is seen that the Lattice energy is not a proper parameter for judging ionic character.

The correct approach in judging the covalent character present in an ionic compound is to follow Fajans' rules. According to this rule, $\phi _{cation}$ is inversely proportional to $r_{cation}$ and directly proportional to $Z_{cation}$ Here, $Z_+$ for all the cation is same. But radius of $\ce{Li^+}$ is smallest and ionic radius gradually increases from $\ce{Li^+}%$ to $\ce{Cs^+}$. So, $$\ce{$\phi$_{Li^+} &gt; $\phi$_{Na^+}  &gt; $\phi$_{K^+}  &gt; $\phi$_{Rb^+}  &gt; $\phi$_{Cs^+} }$$ Here  $\phi$ is the measure of polarising power of cation. As, the value of $\phi$ increases, the polarising power increase and thus the anion's electron cloud gets attracted towards cation nucleus which tends to form a kind of overlap between the orbitals of cation and anion, which increase covalency and decreases ionic character.

So, according to Fajans' rules, increasing ionic character (i.e. more covalency to less covalency) is, $$\ce{LiF &lt; NaF &lt; KF &lt; RbF &lt; CsF}$$