So I'm not sure I fully understand this game.
Is the doctor able to "infect" non-immune persons? If so, I haven't seen it anywhere in the description.
If the Doctor tries to kill anyone that isn't the Immune, then the Doctor loses immediately.
Honestly at any rate I don't see any point to lynching at all in this game. The more we mislynch, the better chances the Doctor wins. They can't actually kill, so we may as well NL until we can be absolutely certain on someone. Granted, that comes with the Doctor getting more information to lead to a better decision on who to kill, but that would happen even if we did lynch.