Lift
Middle English: from Old Norse lypta, of Germanic origin; related to loft.
wiktionary
From Middle English liften, lyften, from Old Norse lypta(“to lift, air”, literally “to raise in the air”), from Proto-Germanic *luftijaną(“to raise in the air”), related to *luftuz(“roof, air”), perhaps from Proto-Indo-European *lewp-(“to peel, break off, damage”) or from a root meaning roof (see *luftuz). Cognate with Danish and Norwegian Bokmål løfte(“to lift”), Norwegian Nynorsk and Swedish lyfta(“to lift”), German lüften(“to air, lift”), Old English lyft(“air”). See above. 1851 for the noun sense "a mechanical device for vertical transport".
(To steal): For this sense Cleasby suggests perhaps a relation to the root of Gothic 𐌷𐌻𐌹𐍆𐍄𐌿𐍃( hliftus) "thief", cognate with Latin cleptus and Greek κλέπτω(kléptō)) [1]
From Middle English lifte, luft, lefte(“air, sky, heaven”), from Old English lyft(“atmosphere, air”), from Proto-West Germanic *luftu, from Proto-Germanic *luftuz(“roof, sky, air”), from Proto-Indo-European *lewp-(“to peel, break off, damage”).
Cognate with Old High German luft(“air”) (German Luft), Dutch lucht(“air”), Old Norse lopt, loft(“upper room, sky, air”). More at loft.
etymonline
lift (v.)
c. 1200, "elevate in rank or dignity, exalt;" c. 1300, "to raise from the ground or other surface, pick up; erect, set in place," also intransitive, "to rise in waves;" early 14c., "remove (someone or something) from its place," from Old Norse lypta "to raise" (Scandinavian -pt- pronounced like -ft-), from Proto-Germanic *luftijan (source also of Middle Low German lüchten, Dutch lichten, German lüften "to lift"), a Proto-Germanic verb from the general Germanic noun for "air, sky, upper regions, atmosphere" (see loft (n.)), giving the verb an etymological sense of "to move up into the air."
Intransitive sense of "to rise, to seem to rise" (of clouds, fogs, etc.) is from 1834. Figurative sense of "to encourage" (with up) is mid-15c. The meaning "steal, take up dishonestly" (as in shoplift) is 1520s. Surgical sense of "to raise" (a person's face) is from 1921. Middle English also had a verb liften (c. 1400). Related: Lifted; lifting.
lift (n.)
mid-14c., "a man's load, as much as a man can carry;" late 15c., "act or action of lifting," from lift (v.). Figurative use from 1620s. Meaning "act of helping" is 1630s; that of "cheering influence" is from 1861. Sense of "elevator, hoisting machine to raise or lower between floors of a building" is from 1851; that of "upward force of an aircraft" is from 1902. Meaning "help given to a pedestrian by taking him along his way in a vehicle" is from 1712. As a dance move, from 1921. Sense of "heel-lift in a boot or shoe" is from 1670s.
The word once had a twin, Middle English lift "the air, the atmosphere; the sky, the firmament," from Old English lyft "air" (see loft (n.)).
