The public board I cover has noticed a meeting where I think they are going to fire an employee. They also have an executive session noticed—can they discuss character and competence in an executive session?

Yes, unfortunately they can. As long as the board votes 2/3 to go into executive session, the board can discuss the character and competence of an employee in an executive session. They can’t, however, fire the employee in that session: they have to emerge from the session and take a public vote in accordance with the Open Meetings Law. Notably, the employee has the right, under La. R.S. 42:17(A)(1), to require that the discussion of their character and competence be held in public.