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Related to button lip: button one's lip, button your lip, Bottom lip
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.
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.