That is an excellent point I never thought about.
Maybe Lieberman just had enough.
I'm totally speculating here, but it's always been my perception that what drove Lieberman out of the Dem party is the fact that, as a Jew, he has a highly realistic understanding of the Islamofascist threat. He accurately perceives that the Dems neither believe in the threat nor are willing to fight it. Add to that their historic support for the "palestinians" and opposition to Israel, and his decision is completely understandable to me. Lieberman may be a liberal on every other issue, but to him, I believe, the anti-semitic threat is the most important one.