This thread has been useful for me.
I have a reputation for being excessively severe on paladins. The paladin in my last game still complains about my hyper-strict rullings on falling from grace.
[I made one fall from grace for attacking a good ally who was trying to help him, when he was as drugged, hallucinating and under mind control. His god (who was NG and not the god of who arbitrates on Pally matters) appeared to him, told him she still loved him and he would always had a place in heaven and told him about a quest that would help him reclaim his paladin hood.]
We still talk about what happened and I think that it really depends on your world and some discussion of allignment.
People in the thread have made some interesting assumptions. I think you DM needs to decide certain things.
1. Does lawful mean you are a legal representative of the government?
If you are, and you broke the law killing someone (either without a fair trial, or because child molestation isn't punishable by death in your world) then you probably fell from grace.
2. Does lawful mean "extremely honorable". I.e. you will never attack a foe from behind because you feel that it is dishonorable -regardless-. Do you feel that all crimes are ultimately arbitrated by the gods, who make their will known by allowing one person to walk away from a dueling match alive (I think this is a greek concept, but I could be wrong).
If so you're probably cooked too.
3. Does lawful just mean that you want their to be order, for people to stay in their roles?
If so then you have a criminal, who is deviating from their social role and disrupting harmony. And killing him is just fine.
(Though people with more expertise in the setting will probably step in to comment: this, btw, was the LG as represented by the you-will-conform Harmonium in Planescape).