Lansky was an associate to the Genovese crime family, so he kicked up to the Genovese crime family, and grew up in New York as a kid, so he was more American and with the Jews instead of with the Vor and other groups from the USSR. You can find a whole list of Jews, Russian, Ukrainians, and other USSR groups that were associates to one of the Italian families.

Agron was the first to be cut lose and go on his own to form his own group with the blessing of the Genovezi family to back him up and the 5 families agreed. (Paul Castellano, Tony Salerno, and Anthony Corallo at least)