No one has to quit. He could have stuck it out until it blew over (and it would). I always felt he cut and ran too quickly. He has no right to whine about anyone 'dumping' him when he was the one that chose to leave.
You're right: Lott stepped down. He was not replaced by Frist in a head-to-head challenge. GWB favored Frist. Let's hope that this silly outburst from Trent registers on Tom DeLay, and he will not follow the Lott route to oblivion and irrelevance.