(Anglo-Saxon, lippe, the lip.)
To curl the lip. To express contempt or disgust with the mouth.
To hang the lip. To drop the under lip in sullenness or contempt. Thus Helen explains why her brother Troilus is not abroad by saying, “He hangs the lip at something.” (Act iii. 1.)
“A foolish hanging of thy nether lip.” —Shakespeare: 1 Henry IV., ii. 4.
To shoot out the lip. To show scorn.
“All they that see me laugh me to scorn. They shoot out the lip; they shake the head...” - Psalm xxii. 7.
Source: Dictionary of Phrase and Fable, E. Cobham Brewer, 1894