Is it farther or further?
1761, "any disabled person or thing;" especially Stock Exchange slang for "defaulter."
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."
A public official or administration serving out a term in office after having been defeated for reelection or when not seeking reelection.
: lame-duck presidentnoun phrase
[political sense attributed to Vice President Andrew Johnson, referring to a Colonel Forney]