Good? Definitely good.
Lawful or chaotic?
Given his extreme adherence to a code of honor (No killing, torturing, etc) I can't see him as being Chaotic.
The fact that he breaks and bends laws is pertinent, but in the non-realistic world of comic books where his vigilantism is openly condoned by Commissioner Gordon, who is a definitive by-the-book cop, it can be argued that his particular extra-legal behavior can be considered officially condoned. If so he isn't quite the law breaker any random would-be vigilante who commits the same violent and illegal acts (assault and battery, breaking and entering, etc.) would be labeled as.
Yet, the very fact that he IS breaking laws to do what he does mitigates the Lawful aspect somewhat, though mostly as pertaining to society's rules.
This reminds me of conflict most people have with paladins in D&D: Most people look at Lawful Good characters as do gooders, but when they think of paladins they mentally classify them as Black and White, Lawful Stupid types. DM's who view paladins in this manner are always a moment away from stripping a paladin of his/her status unless they act like unthinking robots, i.e. Lawful Stupid. Such people fail to consider the fact that the Lawful aspect does not utterly dominate the Good aspect, and act like a paladin should feel obliged to uphold and carry out any law, simply because it's the law, even if the law is something like: "Anyone caught stealing will be publicly tortured and executed, even if the thief is a starving two year old child."
In Batman's case we have a character who's diamond hard principles and code of honor sometimes conflict with existing laws.
I'd say he qualifies as Lawful (with Neutral tendencies) Good.