Sure Lieberman has the right to become an independent or join the Bullshit Moose party or whatever he wants to do. But his latest actions demonstrate a contempt for the Democratic primary process put into place in Connecticut, and threatens the integrity of the whole system. Lieberman's setting a precedent which should probably lead to a revision of Connecticut's ballot access laws to prevent such a thing from happening. You shouldn't be allowed to simultaneously run on a primary ballot and pull petitions to put yourself on the general ballot under the Bullshit Moose party. It makes a mockery of the primary system, and will make the already-almost-impossible task of removing an incumbent in a political primary that much more difficult.
If Lieberman was a noble man, he'd have made his choice: run in the primary or run as an independent. Instead, he's decided that all incumbents in Connecticut should leave themselves the opportunity for a "do over." Pathetic.