bond - Why is Aluminium Chloride a Lewis Acid if it's an ionic compound?

In my textbook it says in the reaction $\ce{AlCl3 + Cl- -> AlCl4-}$, Aluminium Chloride ($\ce{AlCl3}$) has six valence electrons and accepts a lone pair from $\ce{Cl-}$, but wouldn't that mean the aluminium atom covalently bonded with the three chlorine atoms to get six electrons (which is wrong as it's ionic)?