To me killing is fine as long as the circumstances mean that you'll have to make that choice. Like a cop who is surrounded by a gang of killers and he shoots in self defense. The only type of killing I dislike is when you kill out of hate like if say Dr. Light says something to someone like Diana and she loses her self control and outright kills him, that I have a problem but if he starts making threats and Diana keeps a level head about everything and understands that he will carry them out so she kills him. That I don't have a problem.
I feel that out of the Big 3 Batman would have been most fine with her killing Maxwell Lord. I mean, yeah, he might be uncomfortable with it but he is a detective he can't let his emotions get the best of him. He is suppoused operate according to logic, evidence and motive. Those are the things he looks for when solving a crime. He might be uncomfortable with the killing but he should understand 'why' she did it. He should understand that given the circumstances she did the best she could.