Now where is Lott going to rebuild his name? Can he do it from the private sector? Not a chance. He needs to stay in the Senate in order to build his name back and establish some kind of legacy.
If he was samrt, which, unfortunately he's not, he'd negotiate his resignation with the Senate so that he has a nice high profile committee chair from which he can use to prop up his reputation and rebuild his power base. In 5-10 years this will all blow over and if he stays in the Senate that long, he can re-estabish himself to a position of leadership.
If he leaves the Senate, then he might as well leave wearing white sheets and a Red Coat, because he'll forever be known as a racist Benedict Arnold, and after he leaves no one will mention his name again.
It's up to Lott as to what his legacy will be. If he has any brains, he'll voluntarily remove himself from leadership and quietly take his seat in the Senate.