I see no problem here. The man can endorse whoever he wants.
It's not just the endorsement itself, but the way in which he continues to maintain a pretense of still being a Democrat. I hate the term "DINO" when it's misused, but in Lieberman's case, he certainly seems to be going down the route of Zell Miller.
I consider it ridiculous that people support those in the same party simply because they are in the same party. Lieberman's endorsement is a bold move to say the least, but it's one I respect more than supporting a candidate simply because of party affiliation.