Not sure you're right. He is a Demorat, to be sure, but I get the feeling he's not happy with his Party. He may still entertain some aspirations of leadership within his Party, but his position on several issues is more moderate than most of his colleagues'.
I still feel that someday he'll switch Parties.
Lieberman's voting record over the last two years as rated by the ACU is 0% conservative.
Lieberman, on occasion does talk conservative. Possibly, that's why you might think he is more conservative, but he's -- not.