Old English lippa "lip, one of the two sides of the mouth," from Proto-Germanic *lepjan (source also of Old Frisian lippa, Middle Dutch lippe, Dutch lip, Old High German lefs, German Lefze, Swedish läpp, Danish læbe), from PIE *leb- "to lick; lip" (source also of Latin labium). French lippe is an Old French borrowing from a Germanic source.
Transferred sense of "edge or margin of a cup, etc." is from 1590s. Slang sense "saucy talk" is from 1821, probably from the expression move the lip (1570s) "utter even the slightest word (against someone)." To bite (one's) lip "show vexation" is from early 14c. Stiff upper lip as a sign of courage and struggle against despondency is from 1833. Lip gloss is attested from 1939; lip balm from 1877. Related: Lips.