I'd actually say that while an individual who refuses to kill children can still be evil, this is not necessarily indicative of Chaotic or Lawful behavior. At the very least, I'd say Chaotic and Lawful Evil each are each just about as likely to have a compunction against it. Neutral Evil, on the other hand, I'd see having the least problem with it.
The why's on the other hand, would be different.
In a Donner party or waterskin situation, for instance, I'd say any evil character will be just about as likely to resort to the child eating or depriving the kid of water as any other form of evil-aligned character. All ultimately put themselves above others. It's just that each will justify it in their own way. LE: The child likely wouldn't have survived on his own, anyway, and it's better that one of us died than both. NE: I figured no one would find out, anyway, and he'd have done the same to me if he could have. CE: It was me or him, simple as that.
Likewise, a Chaotic Evil individual may be less likely to kill a kid because he feels a child in no way threatens his ability to do what he wants. He realizes he could kill children, but doesn't do so for the simple fact that they cannot stop him from doing what he wants anymore than he lets them - and thus restricts himself from killing kids because it's his decision and no one elses.
Whereas a Lawful Evil individual may be more likely to kill a kid as a child is easily dominated and put into a subservient position, therefore, barely worth consideration.
And for what it's worth, while I don't necessarily believe Lawful fully equates to law-abiding, I do believe it equates, to some degree, towards conforming and working within the system to change it, acting on the desires of others over their own at times, whereas a Chaotic individual acts by their own beliefs for the most part, often running counter to society. Both have as much of a likelihood for having a code of honor, and a solid one at that. I'll even go so far as to say that, in some cases, two individuals with drastically different alignments can act in nearly the exact same way. All that differs is their motivation, and just where they're located (in affluence, in a city whose alignment tendencies favor or disfavor those of the character, and so on).
Edit: Spelling