I don't think Paul Vario was ever the boss of the Lucchese's. I know in the movie Henry says he was the boss over everyone in the neighborhood.. maybe that's what he was talking about in Gangsters and Goodfellas?

Anyways, here's the list of the bosses around that time, to now:

Gaetano Lucchese - 1953 to 1967
Carmine Tramunti - 1967 to 1974
Anthony Corallo - 1974 to 1987
Vittorio Amuso - 1987 to 1992
Joe DeFede - 1992 to Present