Is HCl a lewis base?
The strength of Lewis acids relative to your Lewis base has been commented on. A fuller answer to your question needs to include the Lewis acid you are considering.
The original Bronsted-Lowry theory of comparing acidity and basicity, or acids and bases, involved $\ce{H^+}$ and $\ce{OH^-}$ and the transfer of a proton.
The broader Lewis theory allowed consideration of other cations besides the proton as acids, and other nucleophiles than hydroxide ion to be bases. So water can be considered a Lewis acid relative to chloride ion because $\ce{H2O}$ hydrates chloride ions by hydrogen bonding. And water is a Lewis base relative to metal cations because water hydrates the metal ions through electron donation from oxygen.
So the answer to the question is yes and no. Yes, $\ce{HCl}$ can be considered a Lewis base - relative to a very strong acid, as mentioned in the comments - but in the ordinary world, I would not first think of $\ce{HCl}$ as an alkali. Stretching the word &quot;base&quot; by adding &quot;Lewis&quot; in front of it needs more, like adding the reference acid, to make the comment clear rather than confusing.