Often, no. There's a relevant specific fee-recovery mechanism [0] in some, not all, states, because this class of lawsuit acknowledged as being problematic, as being an effective way to silence 1A-protected speech. The deeper problem is that litigation is extraordinarily expensive in the US, and generically easy to abuse as an intimidation weapon—for rich entities to use against those who can't afford lawyers; or for fanatics to use against normal risk-averse people who don't want lawsuits–don't value whatever it is the fanatic is fanatic about, highly enough to go to court to argue it.

[0] https://en.wikipedia.org/wiki/Strategic_lawsuit_against_publ...

To my (totally uninformed) eyes it looks like maybe this could count as a SLAPP suit [1], in which case there's a possbility for a counterclaim for legal costs. However, Massachusetts apparently has "much weaker anti-SLAPP laws" [2] (than California, in the context of the article)

[1] https://en.wikipedia.org/wiki/Strategic_lawsuit_against_publ...

[2] https://www.vox.com/future-perfect/23841742/francesca-gino-d...

Sadly it doesn't work like that but even that wouldn't be fair. If you lose the defamation as the plaintiff you should be forced to pay the full amount you were suing for to the defendant. Or even a multiple of that.