If he loses the primary but wins the general, instead of being Sen. Lieberman (D-CT) (or even (I-CT), he’ll be Sen. Lieberman (Lieberman-CT)! 
That’s interesting - I guess we’ll find out what it means by Aug. 9.
Looking at the MOEs for the D/R/I breakdowns in the poll I linked to, the MOEs for D’s and I’s are about the same, and the MOEs for R’s are a bit bigger. Which means they polled about as many D’s as I’s, and somewhat fewer R’s. Theoretically, that should reflect the party distribution of Connecticut residents, but I’d classify this data point as being suggestive but hardly definitive.
Still, I’ve heard from other sources besides you that Connecticut has an unusually high proportion of independent/unaffiliated voters, and if you folks have a 3-way race in the general, they’ll clearly be the swing bloc.