last (adj., adv.) Look up last at Dictionary.com
"following all others," from Old English latost (adj.) and lætest (adv.), superlative of læt (see late). Cognate with Old Frisian lest, Dutch laatst, Old High German laggost, German letzt. Meaning "most recent" is from c.1200. The noun, "last person or thing," is c.1200, from the adjective. 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.
last (v.) Look up last at Dictionary.com
"endure, go on existing," from Old English læstan "to continue, endure," earlier "accomplish, carry out," literally "to follow a track," from Proto-Germanic *laistjan "to follow a track" (cognates: Gothic laistjan "to follow," Old Frisian lasta "to fulfill, to pay (duties)," German leisten "to perform, achieve, afford"), from PIE *leis- (1) "track, furrow" (see learn).

Related to last (n.), not to last (adj.). Related: Lasted; lasting.
last (n.) Look up last at Dictionary.com
"shoemaker's block," from Old English læste, from last "track, footprint, trace," from Proto-Germanic *laist- (cognates: 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," Old English læran "to teach"); see last (v.).