Last
Old English latost (adverb) ‘after all others in a series’, of Germanic origin; related to Dutch laatst, lest and German letzt, also to late.
wiktionary
From Middle English laste, latst, syncopated variant of latest.
From Middle English lasten, from Old English lǣstan, from Proto-Germanic *laistijaną. Cognate with German leisten(“yield”).
From Old English læste, Proto-Germanic *laistiz. Compare Swedish läst, German Leisten.
From Middle English last, from Old English hlæst(“burden, load, freight”), from Proto-Germanic *hlastuz(“burden, load, freight”), from Proto-Indo-European *kleh₂-(“to put, lay out”). Cognate with West Frisian lêst, Dutch last, German Last, Swedish last, Icelandic lest.
etymonline
last (adj.)
c. 1200, "latest, final, following all others," a contraction of Old English latost (adj.) "slowest, latest," superlative of læt (see late); in some uses from late (adv.). Cognate with Old Frisian lest, Dutch laatst, Old High German laggost, German letzt.
Meaning "last in space, furthest, most remote" is from late 14c.; meaning "most unlikely or unsuitable" is from mid-15c. Meaning "most recent, next before the present" (as in last night, last September) is from late 14c.; latest would be more correct, but idiom rules and the last time I saw her might mean the most recent time this hour or the final time forever.
The biblical last days ("belonging to the end") is attested from late 14c. Last hurrah is from the title of Edwin O'Connor's 1956 novel. Last word "final, definitive statement" is from 1650s. A dying person's last words so called by 1740. As an adjective, last-minute attested from 1913. Last-chance (adj.) is from 1962. Expression if it's the last thing I do, expressing strong determination, is attested by 1905.
last (v.)
"endure, go on existing," from Old English læstan "to continue, endure," earlier "follow (a leader), accomplish, carry out, perform," from Proto-Germanic *laistjan "to follow a track" (source also of Gothic laistjan "to follow after," Old Frisian lasta "to fulfill, to pay (duties)," German leisten "to perform, achieve, afford"), from PIE root *lois- "furrow, track." It is related to last (n.1), but not to last (adj.). Related: Lasted; lasting.
last (n.1)
"wooden model of a human foot used by shoemakers," from Old English læste "shoemaker's last," earlier last "track, footprint, footstep, trace," from Proto-Germanic *laisti- (source also of Old Norse leistr "the foot," Middle Dutch, Dutch leest "form, model, last," Old High German leist "track, footprint," German Leisten "last," Gothic laistjan "to follow"), related to Old English læran "to teach," from PIE root *lois- "furrow, track."
last (n.2)
late Old English, "the last or final man, object, time, etc.," from last (adj.). From late 14c. as "most recent person, latest comer." Also in Middle English as a noun, "duration" (early 14c.), from the verb. Phrase at (the) last is from c. 1200; extended form long last is from 1520s. To the last is from c. 1400.
last (adv.)
c. 1200, "most recently;" early 13c., "finally, after all others" (contrasted to first), contraction of Old English lætest (adv.), superlative of late (see late).
