die Lippe
lip
One of the two soft, movable edges of the mouth in humans and animals.
Sie hat sich auf die Lippe gebissen, als sie die schlechte Nachricht hörte.
She bit her lip when she heard the bad news.

lip
Loading your saved state.
lip
One of the two soft, movable edges of the mouth in humans and animals.
Sie hat sich auf die Lippe gebissen, als sie die schlechte Nachricht hörte.
She bit her lip when she heard the bad news.

In everyday language, 'Lippe' (lip) is often used in fixed expressions that describe physical reactions or feelings. Common ones are 'sich auf die Lippe beißen' (to bite one's lip, out of nervousness or to avoid saying something) or 'sich die Lippen lecken' (to lick one's lips, as a sign of appetite or anticipation).
Er biss sich auf die Lippe, um nicht zu lachen.
He bit his lip so he wouldn't laugh.
The idiom 'an jemandes Lippen hängen' means to listen to someone extremely attentively. The person being listened to is in the dative.
Die Studenten hingen an den Lippen des Professors.
The students hung on the professor's lips.
The idiom 'eine dicke Lippe riskieren' is colloquial and means to be cheeky or mouthy. It is often used as a warning.
Wenn du hier eine dicke Lippe riskierst, bekommst du Probleme.
If you get lippy here, you'll have problems.
You can always recognize this meaning from context. When containers like 'Glas' (glass), 'Tasse' (cup), or 'Topf' (pot) are being discussed, it refers to the upper rim.
Die Tasse war so voll, dass der Kaffee über die Lippe lief.
The cup was so full that the coffee ran over the rim.
mouth
'der Mund' and 'die Lippe' are both part of the face and are very close to each other. 'Der Mund' means the whole opening used for eating, drinking, and speaking. 'Die Lippe' means only the soft edge of the mouth, that is, the upper or lower lip. Learners may confuse the words because you often see or mention both together. As a practical rule: when it is about speaking, eating, or the opening, 'Mund' fits. When it is about the edge, an injury there, or lipstick, 'Lippe' fits.

Nach dem Sturz blutet Lenas Lippe ein wenig.
After the fall, Lena's lip is bleeding a little.
Beim Zahnarzt muss Tom den Mund weit öffnen.
At the dentist, Tom has to open his mouth wide.