i think the fact that lieberman's committee chairmanship is being decided by secret ballot will probably work to lieberman's benefit. on the one hand, secrecy will give senators cover for voting against someone who they may have good relations with as a friend and colleague. on the other hand, secrecy will allow senators to avoid accountability with the democratic base if they're inclined to give their old friend and colleague a pass.
between those two possibilities, it seems more likely that senators will favor personal connections over accountability. lieberman may end up losing some minor perks as a token penalty, but i predict that he will remain chair of the homeland security committee.
...rumor has it that they cut a deal for lieberman. vote or not, they will make sure that lieberman keeps his homeland security chairmanship but lose some token subcommittee chair or chairs. as i said before there were good pragmatic reasons for dealing with lieberman in 2006. but those reasons don't apply anymore. the democrats would lose nothing by throwing him completely out of the caucus. but it looks like that's not how things will go.