I think Lieberman is honest and will not be turned by dangling goodies in front of him. He could be turned, perhaps, by consideration of the difference in integrity between the two parties.
I think a lot will depend on how the 'Rats treat him now. He may not be influenced by the GOP, but he is also keenly aware of how the 'Rats have treated him the past few months. Politically, he is more in line with the GOP than Lincoln Chafee.