1520s, "footman, running footman, valet," from French laquais "foot soldier, footman, servant" (15c.), a word of unknown origin; perhaps from Old Provençal lacai, from lecai "glutton, covetous," from lecar "to lick." The alternative etymology is that it comes via Old French laquay, from Catalan alacay, from Arabic al-qadi "the judge." Yet another guess traces it through Spanish lacayo, from Italian lacchè, from Modern Greek oulakes, from Turkish ulak "runner, courier." This suits the original sense better, but OED says Italian lacchè is from French. Sense of "servile follower" appeared 1580s. As a political term of abuse it dates from 1939 in communist jargon.
dog breed, 1808, from German Pudel, shortened form of Pudelhund "water dog," from Low German Pudel "puddle" (compare pudeln "to splash;" see puddle (n.)) + German Hund "hound" (see hound (n.)). Probably so called because the dog originally was used to hunt water fowl, but in England and America it was from the start mainly an undersized fancy or toy dog with long, curly hair. Figurative sense of "lackey" (chiefly British) is attested from 1907. Poodle-faker, British army slang for "ingratiating male," is from 1902, likely euphemistic.