Twenty-second Amendment to the United States Constitution
Some argue that the 22nd Amendment and 12th Amendment bar any two-term president from later serving as vice president as well as from succeeding to the presidency from any point in the presidential line of succession. Others contend that the original intent of the 12th Amendment concerns qualification for "service" (age, residence, and citizenship), while the 22nd Amendment, concerns qualifications for "election", and thus (strictly applying the text) a former two-term president is still eligible to "serve" as vice president (neither amendment restricts the number of times an individual can be elected to the vice presidency), and then succeed to the presidency to serve out the balance of the term (though prohibited from running for election to an additional term).
Lame duck (politics)
The term "lame duck president" traditionally is reserved for a president who is serving out the remainder of their term after having been defeated for re-election. In this sense, the following presidents, since the twentieth century, have been lame ducks: William Howard Taft, who was defeated for re-election in 1912; Herbert Hoover, who was defeated for re-election in 1932; Gerald R. Ford, who was defeated in 1976; Jimmy Carter, who was defeated for re-election in 1980; and George H. W. Bush, who was defeated for re-election in 1992. To date, he is the last sitting president to lose in a re-election bid.