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button (one's) lip
To be quiet. Often used as an imperative. Hey, button your lip! We don't need to hear any more out of you today! Julie knew better than to speak up when her father was so angry, so she buttoned her lip for the moment.
Farlex Dictionary of Idioms. © 2015 Farlex, Inc, all rights reserved.
button (up) one's lip
Fig. to stop talking. (Fixed order.) Please button up your lip! Will you button your lip? I don't want the news to get out.
McGraw-Hill Dictionary of American Idioms and Phrasal Verbs. © 2002 by The McGraw-Hill Companies, Inc.