IMO at the very least the case is a lot more nuanced than you're making it out to be. For example: the fired professor was propagating conspiracy theories about Seth Rich. From the free speech angle, sure, she's free to say whatever she wants. But if you're a journalism professor and you aren't able to tell when something being propagated in the media is a baseless conspiracy theory, what does that say about your ability at your job? And as a teacher? It is not flat out wrong to fire someone for engaging in actions that cast doubt on their professionalism. At the very least it's open for debate.
I think there's an interesting debate to be had over her having done this anonymously: if she separated it from her professional persona is she less culpable in a professional sense? Personally I'd still argue no, but I think this is why she's targeting the Lab and not her employer: it's a lot easier to argue that unmasking her (thus combining her anonymous and professional identities) was wrong than to argue that firing her was wrong.
It seems their argument is going to be centered around one particular post expressing an anti-Muslim sentiment. Benton said she wrote it, she said she did not, thus he defamed her. All the posts were made under the same Disqus account so she might have a hill to climb in proving that it wasn't her. I'm very far from a lawyer but this feels like a case designed to set the professor up as a cause célèbre on the right rather than one designed to win.