The whole point of the endorsement is to help Clinton. Droopy Joe owes her a big one after she threw a big rally for Joe before the CT primary in '06.
In NH, independents can vote in either primary. McCain's popularity in NH is among the independents. So is Obama's. They're chasing the same voters. This is Joe's way of paying Clinton back. Anything that helps McCain hurts Obama and a direct endorsement by Lieberman wouldn't help Clinton among Democrats.