When it comes to the NY families, "lieutenant" was never an official rank within the Mafia. No boss called his underlings for lieutenants.
The group leaders within a Family were called caporegime or capodecina. These terms got corrupted by younger, liberal members into "captains" possibly already in the 1950s when the new generation of mafiamembers no longer "revered" the old old Mafia tradition.
The word lieutenant's transition from having been (and still is, of course) a rank designation within the military to one that describes a rank within the Mafia is, I think, a blunder from journalists who described gangsters in general and their underlings. So it stuck.