We found one dictionary that defines the word hang one's lip:

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1. hang one's lip: Wiktionary

Definitions from Wiktionary (hang one's lip) ▸ verb:  To be sullen or sulky. ▸ Words similar to hang one's lip ▸ Usage examples for hang one's lip ▸ Idioms related to hang one's lip ▸ Wikipedia articles (New!) ▸ Words that often appear near hang one's lip ▸ Rhymes of hang one's lip ▸ Invented words related to hang one's lip