He gets a free pass

The Mikhail Bakunin of Nickelodeon cartoons.
Which is why this is fictional, and he's allowed to have a narrative story arc.
However, if this was a Nazi SS Officer, who fled to South America, and then went on to redeem himself by [insert narratively compelling redemption story], he'd still be a war criminal.
But again, it's a cartoon, and we don't have to treat his character as if he were an actual Imperial General commanding troops during wars of conquest, especially one from the IJA.
- Pretty big difference in your scenarios there yours has a Nazi war criminal fleeing after the war is ended. Yeah it doesn't really hit as hard when it's after the fact and there's no skin in the game. A person who realizes his nation is wrong and fights to stop his Nation during the war has a lot more redeeming qualities than someone who claims to have changed his mind after the war is over and while they're running and hiding.

There's evidence he was trying to prevent worse things from happening. He hid the last dragons, he joined a extremist group, he was WAY ahead of Azula capturing him, his prison escape plan was likely a long term thought process he already had. Iroh was never going to be fire lord.

He was first in line to be Fire Lord until his son died.
I don't think Iroh would have been as ruthless as his brother. But he did see conquest as a sort of duty.
But then his son died, and he realized that it was all pointless.
- I want them to dive into exactly that in NATLA, more than they already have.
  Maybe it's just me, but I'm really enjoying it as an 'AU' that explores some off-screen scenes and implications from the original. I think people are getting too hung up on it being 'not ATLA' (just like LoK).

People change, we should all learn to see people for who they are, not who they were.

I'm not sure siege is considered a war crime. Isn't that just standard medieval warfare?

The other nations wouldn't see it that way.
There's no central authority, but it's not a machiavellian free-for-all like medeival Europe. The rest of the world was rather unhappy with the Fire Nation's aggression, even in light if the world's long history of warfare. He would be tried for that, no doubt.
And his reputation/nickname is subtext for crimes he did commit but that the cartoon couldn't spell out.
- I mean, that's essentially saying it's a war crime to be in the military during a war. Which is kind of silly to put it like that.
I mean really the existence of war crimes relies on the existence of treaties between the nations defining what those crimes are. Gonna guess the Fire Nation was not a signatory.
- The Nazis weren't signatories to the Nuremberg charter, yet they were judged by it. So there is precedent for judging war crimes without pre-existing law.
No, it's not a war crime that I can find, however we can attribute harm caused to civilians through these actions, such as starvation due to supply lines cut off. So he did some vile shit, had a moment where he realized the error in his ways, then did everything in his power to make things better.
- Except there no evidence of starvation in Ba Sing Se. After all, there was so little impact that the citizens could be convinced that there was no war.
  As to supply lines, earth benders cannot be locked in by a siege. They can create tunnel networks with a literal wave of the hand.
  So you're inventing crimes that didn't exist.
Depends on the culture The Japanese viewed siege tactics as cowardly and armies at the gates would deliver food and supplies to the people in the walls. Ba Sing Se was able to convince it's citizens there wasn't even a war going on, I don't think they were starving or being killed with siege weapons.
Siege warfare of a city is absolutely a war crime.
Additional academic reading on the subject.
- The source you provided makes clear that sieges are lawful provided non-combatants aren't affected (so starving civilians, barring humanitarian aid, etc. makes a siege unlawful). Furthermore, it states that sieges where non-combatants are affected were lawful prior to the 20th century.
  In the context of ATLA, there's not really enough known about the geopolitics of the world to properly gauge whether or not besieging a city is a war crime. The frequency of sieges in the show (North Pole, Ba Sing Se) can't be used as an argument for their legality since they're undertaken by a state that is known for mistreating prisoners of war, disrespecting geopolitical boundaries, and so on. Regardless, you can't judge the Avatar universe by real world law.

Varrick bombed buildings and tried to kidnap a president to start a war for profit and got away with it too.

He did it as a capitalist though so it's no big deal.
If Varrick were real, he would have blown himself up because he had a hissy fit, threw his briefcase at the wall, but forgot there was a bomb in there.

Well he does leave the army and help the opposition so I'd say he redeemed himself hard

Not only does he help the opposition, I'd argue he was one of the most involved people in bringing peace to the world, between everything he did to train Zuko to become a great leader and all the ways he helped team Avatar, I think the world would have turned out far darker if Iroh hadn't existed.

A war crime according to... Who? Is there some treaty or convention that happened? Is there some customary international law that he violated? I can't find the Hague anywhere on any maps in this universe but maybe I missed something.

There is no war

I like how NATLA goes into his "war crimes" more.

And Lu Ten's funeral... I cried over that scene.

There's a lot to not like about live-action atla, but I was there for all the Iroh/Zuko scenes. Kinda like Book 1 of ATLA, to be honest.

I agree, I love the change they made to include the fact that Zuko's soldiers where the same ones he spoke out against sacrificing.

Maybe not war crimes but what he did with June isn't great either

He apologies for that in the comics, though many of the panels feel OOC.
- Which comic is that one from?
- They should have gone back and edited the show rather than do this. The Iroh and June thing was way out of character for Iroh to begin with. Likely some writer that was unfamiliar with the show and took too much inspiration from Master Roshi.

A sige isn't actually a warcrime...