Batman is ridiculously lawful and arguably good. He never breaks his code under virtually any circumstances, and often opposes others not based around how they are harming innocents, but around how they are breaking his code. As far as his goodness is concerned, his intent is mostly to help better society and stop crime at an extreme cost to himself, which is quite obviously good. On the other hand, he is primarily motivated to do so out of revenge in many cases, which is not so good. He also is quite willing to utilize underhanded tactics as long as they don't break his code, which is also not very good. So he's definitely lawful, and either good or neutral depending on what aspects the writer or reader wishes to focus on. For me he's lawful good though.
Edit- and people really shouldn't equate the Paladin code with lawful good, or lawfulness in general. Otherwise, as others have pointed out, the idea of lawful evil makes very little sense.