Here is a post of the extracts from Mississippi law on filling a vacancy in the US Senate - Missippi Law. Governor is Ronnie Musgrove. He will appoint an interim democrat. He then must call a special election. The timing of the election is dependent on the timing of Lott's resignation. If Lott resigns while the Senate is not in session, Musgrove MUST call the election in 90 days. If Lott resigns in Session the special election for Senator will take place on the next regularly held Mississippi General Election which is Nov. 4 2003. (Mississippi's governor & other state offices are up then).
Either way an interim would have to assume office and stand for election in short order. Lott's resigning would not not eliminate the majority, but may cause someone like Chafee to switch. Chafee may not want to switch knowing the GOP will revert back to Senate control even with his switch in less than a year.
Lott IMHO won't resign his Senate seat. One thing he is not is a man of principle. Too much pork to shovel around on the Commerce Committee.