Is there something odd or stilted -- or inadvertently jocular -- about the usage "'I didn't do it,' he lied"? I've seen it used before, in the same contexts that one would see "he said"; but while one would say "he said the answer" we wouldn't usually say (I think) "he lied the answer."
Generally speaking, "lie" is either an intransitive verb meaning "To present false information with the intention of deceiving" (I quote the American Heritage Dictionary here) or a transitive verb meaning "To cause to be in a specific condition ... by telling falsehoods," as in "You have lied yourself into trouble." Is "lie" nonetheless used as a transitive verb, with "X lied Y" meaning "X said Y with the intention of deceiving"? Or, even if "X lied Y" isn't idiomatic, it's nonetheless fully idiomatic to say "'Y,' X lied"?
(Let's set aside the question whether "he lied" violates the "show, don't tell" maxim of fiction writing. Assume that this is in a work of nonfiction, or that otherwise we're not worried about this storytelling principle.)