No. None of her shows lasted anywhere near the 'longest running' status, however, I Love Lucy (1951-1957) does have the distinction of being the first show to be rerun & the longest running show in syndication [e.g. reruns].
View page
Your question can't really be answered due to the fact there are dozens of TV shows that were the longest running before & during 2001 that are still on the air today (as of May 2014) so anything that started before & canceled in 2001 clearly wasn't the longest running in the first place.
View page
Is it the Simpsons
View page
This shows alist of the longest running shows. See link below