Yeah, I wouldn't say Batman is always lawful in the strictest sense. He breaks a lot of society's laws in his pursuit of criminals: he taps phones and hacks computers without a court order, he breaks into buildings without a search warrant to find evidence, and so on. You have to wonder how a lot of the criminals he arrests ever get convicted.
But he never plants false evidence, or lies on the stand to falsely convict anyone. Basically, he only breaks the laws that get in the way of bringing criminals to justice, and all the people he goes after are ones who've broken what he considers the important laws -- the laws against hurting innocent people. So you can argue that he obeys a different set of laws, but he's still lawful under those laws. I certainly wouldn't call him chaotic -- everything he does is pretty highly structured.
And since everything he does is for the purpose of fighting evil, I suppose you could even argue that he's Lawful Good, but not in the sense of the typical paladin who won't break any laws. That may be a limitation of the people who play those paladins, or the DMs who enforce their interpretation of Lawful Good behavior, however. Then again, you could also argue that a man who decides which laws he'll follow and which laws he won't is more Neutral than Lawful. I could see Batman as Neutral Good.
I dunno. I haven't played D&D in so long, I have no real idea how the categories are "supposed" to work these days...