Is the reaction of calcium carbide with water a Brønsted-Lowry acid-base reaction or Lewis acid-base reaction?
We may regard the calcium hydroxide and calcium carbide  as essentially ionic except for the covalent bonding within the anions.  So there is no Lewis reaction involving the calcium.

That leaves the proton transfer, which can be described fully by the B-L theory.  You actually have two reactions, successively forming $\ce{C2H-}$ and then $\ce{C2H2}$.