Lansky himself, and by extension, the men subordinate to him and allied with him directly or indirectly were not known to engage in that, (although I don't doubt some of them may have).

Luciano, Davy Petillo, Jimmy Federico, and the others involved in that case, of "extorting" NYC's whorehouses were not "with" Lansky. And so the record is clear, the vast majority of New York's mafiosi didn't run whorehouses themselves. Most just extorted the operators of cat houses.

There were, or course, many instances of out of state guys (PA, OH, etc), mostly early Camorra (Napolitani) and Societa' Onorata members (Calabrese) who were indeed in the business directly. But Sicilian mafiosi tended to "earn" from it through shakedowns.