Button one's lip is a phrase that means to stop talking or to keep silent about something. There are numerous synonyms for the phrase, each with its own distinctive connotation. To clam up, for instance, implies that someone has become tight-lipped or uncommunicative when faced with a sensitive topic. To hush up suggests an effort to conceal or prevent something from being exposed. To zip one's mouth, meanwhile, intimates the need for quiet or secrecy. All these colorful expressions are useful in conveying one's desire to stay mum or to hold back certain information.
