I'm here to end the reign of giving out free wins based on likability!
Iroh has made it as far as he had because he has kindly grandpa energy and a good head on his shoulders, and keeps coming up against brash young punks. A lich is the opposite of that, with more knowledge and wisdom, and also bunches of spells, and the inherent unkillability that comes not only from being undead but also having a special "ha, can't kill me if I still have this!" trinket stashed away somewhere. Neither is really in a position to dodge anything, and I feel like if they just trade big blasts, the guy with skin in the game is going to suffer from the ol' mortality, giving a win to Lich.
Meanwhile I really can't see The Thing and the regular ol' dog being in a position where either feels comfortable attacking the other, so we'd need some alternate means of resolving this, like I dunno, a contest of endurance or something. Whatever this alternate method is though, at some point tournament organizers are basically being put in a position where they're setting up SOME sort of thing where they're subjecting a grown adult with weird skin and a regular freakin' dog to something unpleasant, whether it's damage of some kind or a long time on a treadmill or whatever, and at some point some sort of animal rights group is going to have to step in and insist they knock that off and let the nice dog just go home, at which point I'm pretty sure The Thing would move on, bearing a grudge against the organizers of all this because really how did we arrive at such a place?