What causes your lip to jump constantly?

Jumpy lip: Stress, anxiety, tremors.

Lip twitch: Constant "jumping", twitching, fasciculations or spasms of the are most commonly caused by stress, fatigue and severe anxiety. Other causes include low potassium, tumor, head trauma, tumor, early onset of bell's palsy or recovery from bell's palsy or a version of hemifacial spasm. With common causes twitch is short lived. With the others, twitching can progress and persist if cause not treated.

Many things: Without more information it would be difficult to tell. The most common causes would be a spasm of the "lip muscles" or orbicularis oris; an electrolyte deficiency (most likely calcium); or a nervous tic. However you should have a thorough history and exam to determine if there are other neurological problems present which could indicate a more serious condition.