This is really interesting. For fun, I went back to the SRD and looked up alignments again and I was surprised by what I read. Somehow, I remember this passage very differently, so I'm posting it here:
Although there is lots of room for interpretation, it seems to me that the fighter (by these definitions) was acting more chaotic (or at least neutral) than lawful. My intepretation of the passage above is that "lawfulness" is more about following the rules, laws and traditions of a society. Personal code and conscience seem to fall under "chaotic."
I think that the word chaotic is misleading. I think many people (including myself from time to time) think of it as random or whimsical, but it might be more about individualism. A chaotic-aligned person might act in a predictible way and have a very well-defined personal code, but it is one that he has decided for himself, not one handed to him by an authority.
Maybe the fighter should reconsider his alignment.