And/or can Litigious somehow sue Harry via a suit against the university? How would this play out?
It is my experience that anybody can sue anybody for anything. I have heard of professors suing administrators; professors suing the university; administrators suing the school; students suing the school; students suing professors; professors suing chairs; professors suing other professors.
Talking to various people involved, my understanding is that while often the cases are thrown out, the end result is usually a lot of time and money eaten up by attorneys. Thus in some cases the university might settle instead of drawing out a long lawsuit.
I am not sure how likely it is that somebody acting in a official capacity and within more or less reasonable limits could be found personally liable. That is, if Harry sexually harassed or threatened to kill Litigious, that would be one thing; but if Harry just made a bad decision, it is not likely that he would personally be legally liable. Except for the procedural error, it does not seem that Harry did anything illegal. And I am not entirely sure what the procedural error entailed, but even so, it would seem to be not that important since the department voted to give tenure to Litigious.
If Litigious was disciplined for union activity, that would seem to fall under the purview of the NLRB. (Although it is hard to win such cases.) Perhaps Litigious could make a case that the denial of tenure was wrong (e.g., that he was punished for his union activism). I am not sure where Harry comes into this--and it would seem a diversion from any (perhaps) legitimate suit that Litigious might have.
Of course, the real answer is to consult an attorney. But if you pay an attorney enough (or pay the right attorney enough, or find an attorney willing to take on a suit for part of the settlement) they will sue anybody for you. Litigious could probably even find an attorney who would tack on the claim of loss of consortium to the case. The question is, is there any chance of winning.