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.