Middle English, from Old English lifian (Anglian), libban (West Saxon) "to be, be alive, have life; continue in life; to experience," also "to supply oneself with food, procure a means of subsistence; pass life in a specified fashion," from Proto-Germanic *libejanan (source also of Old Norse lifa "to be left; to live; to live on," of fire, "to burn;" Old Frisian libba, German leben, Gothic liban "to live"), from PIE root *leip- "to stick, adhere," forming words meaning "to remain, continue."
Meaning "to make a residence, dwell" is from c. 1200. Meaning "express in one's life" (live a lie) is from 1540s. Intensified sense "have life abundantly, make full use of life's opportunities" is from c. 1600. Related: Lived; living.
To live it up "live gaily and extravagantly" is from 1903. To live up to "act in accordance with, not live below the standard of" is 1690s, from earlier live up "live on a high (moral or mental) level" (1680s). To live (something) down "cause (something disreputable) to be forgotten by subsequent blameless course, live so as to disprove" is from 1842. To live with "cohabit as husband and wife" is attested from 1749; sense of "to put up with" is attested from 1937. Expression live and learn is attested from c. 1620.
According to the Dutch Prouerbe ... Leuen ende laetan leuen, To liue and to let others liue. [Gerard de Malynes, 1622]
1540s, "having life, not dead," a shortening of alive (q.v.). From 1610s of fire, coal, etc., "burning, glowing;" 1640s of things, conditions, etc., "full of active power;" sense of "containing unspent energy or power" (live ammunition) is from 1799. Meaning "in-person, not recorded" (of performance) is first attested 1934. Live wire is attested from 1890, "circuit through which an electric current is flowing;" figurative sense of "active person" is from 1903. Jocular real live "genuine" is from 1887. The older adjective is lively.
A GRIM RECORD -- The death harvest of the "live wire" and "third rail" goes right on. It is not governed by seasons nor, qualified by time. It is the ubiquitous epidemic of electricity, defiant of doctors and ruthless as fate. ["The Insurance Press," Aug. 22, 1900]