"a lie," especially a little one, "a white lie," 1610s, of uncertain origin, perhaps from fibble-fable "nonsense" (1580s), a reduplication of fable (n.).
"tell trifling lies," 1680s, from fib (n.). Seldom, if ever, transitive. Related: Fibbed; fibbing; fibbery.
he told a fib about eating his spinach