Is Batman Lawful Good or Chaotic Good?

Although I'm not the original target of this question, I love Batman and I'll weigh in anyway.

It can be argued both ways, but I rule in favor of Batman being Lawful Good. The answer lies in how one interprets "Lawful". If one interprets lawful being by the book, then Batman is unlawful because he punches people, interrogates people without a badge, unlawfully imprison's people, creates thousands of dollars in property damage, spies on and wiretaps people without a warrant, ignores due process of the law and the courts, presumes guilt without a public trial by peers, etc. Imagine Batman having to wait on Gordon to be deputized and then wait in line to get an arrest warrant signed by a judge to bring in the Joker...

But if you interpret "Lawful" as a morally sound code of honor, then Batman is as lawfully good as Superman is. He is fighting obviously evil villains, never really waivers or doubts what he needs to do, never truly questions which "side he is on", and is fighting the good fight to save Gotham. He realizes he must be tough because the opposition is tough, and the law system put in place is just as corrupt and evil as the villains are.

Of course, a character can be "Lawful Good" and still make mistakes. Batman is human. But it goes without saying that a Lawful Good character can make a mistake, lash out, and kill someone without losing their Lawful Good nature. So the questions like "Has Batman ever killed anyone [yes he has], or would Batman ever kill anyone" are trifle and don't really matter. I don't know where this silly "Lawfully Good characters never kill anyone" rule comes from. Good smites Evil all the time, and vice versa. Good can be just as voracious, stiff-armed, and imposing as Evil.

Batman is doing what we all want to do and not letting the law of the land stop him from carrying out what we all would rationally consider "morally just" in the contexts of his story.