Lansky died in 1983. Once Upon A Time In America was released in 1984.
I know that it was being filmed in 1983 because that year I went down to St. Petersburg Florida to visit my father and on the way home, on our plane, were an actor and actress who at the time were making a mob movie; James Woods ( who I really didn't recognize back then) and Tuesday Weld, who I did recognize.
So there is a possibility that DeNiro did seek an audience with Lansky before filming began. This site claims that DeNiro did request to meet with Lansky.
http://www.gonemovies.com/WWW/WanadooFilms/Misdaad/EnglischAmerica.asp Don Cardi