Among the lithium halides, the most covalent one is

The cation $\mathrm{Li}{}^{+}$ is the same in all four, so only anion size matters. Polarisability increases down the group: $\mathrm{F}{}^{-}<\mathrm{Cl}{}^{-}<\mathrm{Br}{}^{-}<\mathrm{I}{}^{-}$. Hence $\mathrm{LiI}$ has the greatest covalent character.