Lex Luthor was presumed dead in Action Comics #660.
He re-emerged as his son Lex Luthor II (Cameos in Action Comics #670 and properly revealed in Action Comics #672 - "All This and Lex Luthor II")
With the switch being explicitly revealed in Action Comics #678 - "Talking Heads".
I recall he lost his hair as the clone body degraded in the Fall of Metropolis arc around Action Comics #700, and next surfaced in Man of Tomorrow #1 "Past, Present & Future!" where he was rejuvenated.
When Lex Luthor ran for president did the general public believe that it was his "son" Lex Luthor II or was it known to the man on the street that Lex had cheated death and had his brain saved and put into a younger healthier body?
The clone rejuvenation storyline was after Zero Hour, and the presidential campaign was before Infinite Crisis, so it wasn't removed from continuity.