Assertion A states that lithium halides are somewhat covalent in nature. This is a true statement. According to Fajan's rules, although formed between a metal and a non-metal, lithium halides (especially LiI) exhibit significant covalent character. For instance, LiCl is soluble in organic solvents like ethanol.
Reason R states that lithium possesses high polarisation capability. This is also a true statement. The term "polarisation capability" refers to the polarizing power of the cation. The Li$^+$ ion is very small and has a relatively high charge density. This allows it to distort the electron cloud of the larger halide anion to a significant extent.
Connecting the Assertion and Reason: The high polarizing power (polarisation capability) of the Li$^+$ ion is precisely the reason why it can pull the electron density from the anion, leading to a sharing of electrons and thus covalent character in the bond. Therefore, Reason R is the correct explanation for Assertion A.