The Mousetrap did have a run in the 50's, but it was Off-Broadway and wasn't overly successful (at least as compared to its Londan run, still going since 1952!!!).
Edward II -- It may be Marlowe's best play, yet as far as I know, it's never played in a Broadway house. It's a beautiful play, containing some of Marlowe's best poetry.
Titus Andronicus
Coriolanus -- Not sure about that one, I know Papp did it at least once, but Broadway???? Anyone know for sure???
The Lesson -- Was done as a double bill with The Chairs Off-Broadway around 1957 or 1958, but I'm not sure that The Lesson, either individually or in tandem with something else, has been done on Broadway.
Three Tall Women -- Pulitzer Prize
Lazarus Laughed -- Just for the sake of argument -- the play stinks. It's a confusing crashing bore and almost unproduceable (particularly in today's financial climate), but, it is O'Neill from his approaching halcyon days.
BroadwayEd