I'd say that here the problem is more that you are varying the Lawful aspect of their personalities, but the situation as -- simply -- described actually relates more to Good than it does to Lawful. The Law/Chaos axis is essentially no more than "Do you follow your own conscience or do you follow the rules even if they conflict with your own personal feelings?" Lawful characters follow the rules even if they personally, at that point, think that not following the rules will lead to the better outcome as per their other axis, while Chaotic ones follow their own personal judgements even if the rules say otherwise. so, in this case here, speaking strictly on the Law/Chaos axis:

LG: "Was there any law broken? Will I be breaking any law in taking your aid?" (remember that being LG and being a Paladin are not the same thing).
NG: "Hmmm. I don't think I'll be breaking any laws, and it might be worth it to get out of the situation anyway."
CG: "As long as my personal conscience doesn't make me disapprove of you personally, I don't see why I shouldn't help."

But then that does come down to personality, and comes down to how each character FEELS about working with someone who caused the situation and did it with someone who's evil.

A better differentiator would be if the association here would involve breaking the law:

LG: "I'm not going to break the law to get out of this situation. I'll find another way or accept the consequences."
NG: "I don't want to break the law, but if the situation is bad enough ..."
CG: "That it's illegal doesn't say anything about whether or not I should work with you."

But, yes, personality comes into all cases as well, but I think that the reason they all come up the same is that the sitaution calls for a judgement based on the Good/Evil alignment axis, but you're only changing the Lawful one. Think about it for, say, NG, True Neutral, and NE:

NG: "I have a problem working with someone who not only works with evil, but does so wilingly and unapologeticaly" (which doesn't mean that they wouldn't work with them).
True Neutral: "If it works out the way I want, I'll work with anyone".
NE: "... What's the problem?"