Altough it is mentioned in American gangster that Armand Assante's character is the boss of the Lucchese family, he is completely fictitious. He is portrayed as a sort of top boss in the New York underworld, while Tramunti wasn't. For that reason he is more likely based on Carlo Gambino. He also lives in a very similar home as that of Paul Castellano. I don't think the makers of this movie spent much time doing research. As far as I know Frank Lucas did business with the Gambino's and Genovese's (especially Anthony Salerno).

So I think Armand Assante's character is a composition of various gangsters, including Vito and Michael Corleone as the film clearly copied the style of The Godfather. But nevertheless it's a very good movie though.