If Lieberman were to caucus with the Republicans, they would still not take full control of the Senate, despite Vice President Dick Cheney's ability to break 50-50 ties. This is because of a little-known Senate organizing resolution, passed in January, which gives Democrats control of the Senate and committee chairmanships until the beginning of the 111th Congress.So while the despicable Joe can cause some problems, he can't give the Senate to the Republicans.
What's the difference between now and 2001? A small but important distinction. When the 107th Congress was convened on January 3, 2001, Al Gore was still the Vice President and would be for another two-and-a-half weeks. Therefore, because of the Senate's 50-50 tie, Democrats had nominal control of the chamber when the organizing resolution came to a vote. With Dick Cheney soon to come in, however, Democrats allowed Republicans to control the Senate in return for a provision on the organizing resolution that allowed for a reorganization of the chamber if any member should switch parties, which Jeffords did five months later. There was no such clause in the current Senate's organizing resolution.
Hilzoy at Obsidian Wings goes on the describe the whole thing about "Senate Organizing Resolutions."