We don't know that. As I read the Mississippi statutes, if Lott resigns from the Senate in calendar 2002, the Governor of Mississippi must schedule a special election within 90 days to name his replacement. He could appoint an interim Senator, but only for 90 days. Another window occurs in late 2003; if Lott resigns in, say, September or October of 2003, his replacement would be chosen in the general election in November.
I do not know what the risk is of a Democrat winning such an election, but for sure what will not happen is that the current Governor would appoint someone to serve out Lott's term.