When your focus is on you as an individual, rather than a greater whole, how is that lawful? Chaotic people can have strong codes. Two Face has a a particular personal rule even!
I'd say he's CG (usually) with lawful ideals of justice (except Adam West Batman, who is LG). But this is why it's a poor shorthand.
I'd say his focus on his own wants, rather than working to improve the society he claims to want to benefit makes him chaotic. He's a cishet white male billionaire super scientist with 18's in every stat. The idea that he can't change Gotham for the better and improve the system is ludicrous. He's chaotic because he puts nothing above his own personal quest for vengeance. It's worth noting Batman kills people, notably Darkseid. Like the Pirate Code, it's really more of a guideline.