Button One's Lip Meaning
(idiomatic) To remain silent, especially in order to keep a secret or to avoid saying something inappropriate.
Example: 1910, Jim Nasium, "The Baseball League on the Styx," The Sunday Press (Pittsburgh), 15 May, p. 2 (retrieved 19 July 2010):
"Yes," put in Solomon. "I've been tipped off to this guy Mars, and you'd better tell him to button up his lip and not start anything."
1971, Ted Blackman, "Green as team player too," Montreal Gazette, 13 Oct., p. 13 (retrieved 19 July 2010):
"We advised John not to talk, to button his lip, but he talked anyway."
2010, Larry Woody, "Busch Better Heed Burton," FOXNews.com, 1 June (retrieved 19 July 2010):
Busch wisely buttoned his lip and didn't say anything else.