Bite One's Lip Meaning

(idiomatic) To forcibly prevent oneself from speaking, especially in order to avoid saying something inappropriate or likely to cause a dispute.

Example: 1822, Sir Walter Scott, Peveril of the Peak, ch. 49:
  Buckingham bit his lip, for he saw the introduction of Lady Derby was likely to confuse and embroil every preparation which he had arranged for his defence.
1922, F. Scott Fitzgerald, "May Day" in Tales of the Jazz Age:
  He broke off and bit his lip, feeling that he had better subdue the rising anger in his voice.