A lame duck is a man who cannot pay his differences, and is said to waddle off. [Thomas Love Peacock, "Gryll Grange," 1861]Sometimes also in naval use for "an old, slow ship." Modern sense of "public official serving out term after an election" is recorded by 1878 in American English, from an anecdote published in that year of President Lincoln, who is alleged to have said, "[A] senator or representative out of business is a sort of lame duck. He has to be provided for."
Also kynde erreþ in som beestes wondirliche j-schape, as it fareþ in a beest þat hatte lamia, þat haþ an heed as a mayde & body as a grym fissche[;] whan þat best lamya may fynde ony man, first a flatereþ wiþ hym with a wommannes face and makeþ hym ligge by here while he may dure, & whanne he may noferþere suffice to here lecherye þanne he rendeþ hym and sleþ and eteþ hym. [John of Trevisa, translation of Bartholomew de Glanville's "De proprietatibus rerum," 1398]