Yes, Lansbury was nominated for an Oscar for her role, but was up against To Kill a Mockingbird, The Birdman of Alcatraz and The Miracle Worker (she lost to Patty Duke).
The movie was of course withdrawn from circulation for a decade after Kennedy was killed in eerily similar circumstances.
What a year for pictures though: Mutiny on the Bounty, Lawrence of Arabia, The Music Man, Days of Wine and Roses, Hatari!, The Longest Day, Whatever Happened to Baby Jane, Tender Is The Night, Tara's Bulba.