FWIW, Lester Munson (who is great, even as an ESPN employee) wrote a Q&A about the possibility of a lawsuit. :
Q: The Patriots' rebuttal Thursday was aggressive and detailed. What was the purpose of this attack on Goodell and the investigation?
A: It is possible the Patriots' rebuttal will become the foundation for a lawsuit against Goodell and the league. But it is more likely that the purpose of the rebuttal was a form of damage control. It offers material for the Patriots' true-believer fans to use as they continue to support their beloved team.
It might diminish the effect of the investigation's assault upon the team's reputation in its market. But it's highly unlikely owner Bob Kraft will file any litigation against the NFL. If he filed a lawsuit, he would join the late Al Davis and Donald Sterling as the only sports team owners to sue their fellow owners. Kraft does not want to be in any group that includes Davis and Sterling.
Q: What advantages, if any, does Brady enjoy in this appeal?
A: In reality, just the notion that it cannot get any worse for him.
Whether the arbitrator is Goodell, Henderson or an independent person, the arbitrator cannot increase the suspension. If the arbitrator looks at all the evidence and concludes that Brady was guilty of a form of cheating that affected the integrity of the competition in the most successful sports enterprise in America, the arbitrator could not suspend Brady for more than four games. If the arbitrator had the power to actually increase a penalty, well, Brady and the NFLPA might not have filed an appeal.
http://espn.go.com/espn/otl/story/_/id/12888612/tom-brady-nflpa-cannot-win-appeal-filed-deflategate
He also thinks there's no way the NFLPA has a chance in court. I'm not sure I agree with him, but he's way smarter than I am, so.
I'm a biased Pats fan, and I'm not well versed in the applicable area of law, but it's just difficult for me to believe that an independent arbitrator would look at all of the facts, and how this has been handled by both sides from the start, and determine that 4 games was a reasonable suspension. Maybe the standard is higher than that -- maybe the decision needs to have been without merit, or arbitrary and capricious, or something like that.
I still think 4 games would get knocked down on that basis. We'll see, I guess.
The bottom line here for me is that Brady is being punished for the past conduct of his organization, and the stated basis for that punishment is his general awareness of rule breaking by other people in the organization. None of that is a valid basis for punishing Brady personally.
If the court sees it the same way, I can't imagine the punishment standing.