The Lieutenant 1975; the shortest running musical to have been nominated for Best Musical. 9 performances and maybe a week of previews at the Lyceum. It was a lousy year. The other nominees were Mack & Mabel, Shenandoah and the winner, The Wiz. It was also nominated for book, score and lead actor who was a very talented unknown named Eddie Mekka, later to achieve celebrity on Laverne and Shirley.
Plot: well, this show was suggested by the Calley massacre in Vietnam. [I need to pause and quote Anna Russell: "I'm not making this up you know."] I think there was one woman in the cast and the rest were singing rock-opera soldiers.
This all said, there have been shows that have been a lot worse that played a lot longer. The energy of the cast more than made up for any artistic shortness.
"If my life weren't funny, it would just be true. And that would be unacceptable."
--Carrie Fisher