Lib
late 19th century: abbreviation of liberal.
wiktionary
Abbreviation for various words beginning in lib-.
From Middle English libbe, from Old English lybb, lyb(“medicine, drug, potion, poison, charm”), from Proto-West Germanic *lubi, from Proto-Germanic *lubją(“wort, herb, drug, poison”), from Proto-Indo-European *lewbʰ-, *lewb-(“to peel, break, damage”), from Proto-Indo-European *lew-(“to cut, remove, prune, separate”). Cognate with German Luppe, Lüppe(“salve, ointment, plant juice, medicine, magic”), Icelandic lyf(“medicine, drug”).
From Middle English libben, related to Dutch lubben(“to castrate, emasculate”), Dutch libbe(“a steer”), lubbert(“a eunuch”). Further relation uncertain. Possibly related to Old English *lybbian(“to doctor”), from lybb (see above); or perhaps related to Old English lappa, læppa(“lappet, piece, section, lobe, portion, district”). More at lop.
etymonline
lib (n.)
1969, American English, shortening of liberation, used with possessives, originally in Women's Lib. Colloquial shortening libber for liberationist (n.) is attested from 1971.