This is indeed quite a good question and I cannot do much more than recapitulate some speculative things you might have considered yourself already, but let's see.
First of all to some degree Natalie serves as a distraction to prove that notes are in no way less treacherous than memories, by being presented as "good" while being revealed to be more and more "evil" later on, and thus opposite to Teddy. But still you are right in that she couldn't know about Teddy being the one with the license plate, so either it was a writing inconsistency, sacrificing a bit of logic to the purpose of a nasty revelation about Natalie's character, or we can really find some justification for her actions later in the story (earlier in the movie).
But even at the beginning (of the story -> later in the movie) she showed some compassion for Leonard during his first visit in the bar, when she was about to play a little trick on him with the beer everybody had spit in. She takes the beer away from him once he starts talking about his dead wife as she probably feels a bit guilty seeing that Leonard really got some serious problems.
And while the scene where she got beaten by Leonard and revealed her bad side probably didn't show her from her best side, she was really at a dead end herself at this point, with Dodd chasing her for Jimmy's money and her not knowing if to trust Leonard or if he had anything to do with Jimmy's disappearance. So much of her bad bevahiour in this scene could be seen in the heat of the moment (and maybe even with the intention of provoking a punch from Leonard in order to blame it on Dodd). So I think even then she didn't misuse Leonard just out of bad will or greed, but because she had serious problems herself and was not lying when saying she was threatened by Dodd, even if making up the beating.
Now when Leonard arrives at her house after beating up Dodd she indeed first eagerly and selfishly asks if he killed him. But then she starts to see his "freaky tattoos" and learns a bit more about his dead wife and especially his deep feelings for her and his determination in finding the killer, to which she says "I've lost someone, too". And later they share a night, with Leonard talking very emotionally about his wife and his quest for revenge. And indeed the next morning Natalie says she'll check the license plate. And I think Natalie's behaviour during this whole visit seemed very honest. This is then also continued by her honest enquirings about his memories of his wife, when she gives him the information about the license plate in the bar. (Yet, this is all shown before the reveal about her misusing him later in the movie, so it's maybe hard to say in which way we can trust her depiction entirely or in which way it's deliberately distorted to facilitate the effect of the later revelation).
So while being revealed to have rather bad intentions later in the movie, I think especially this visit by Leonard indeed sparked some feelings in her for him. If not actual emotional feelings for him, then at least understanding of his situation and his quest for revenge, maybe mixed with guilt about misusing him. So I agree with the fact that she's a much more ambiguous character than one (at least I) might think after watching the movie just once and I'd deduce that she really wanted to help Leonard when she checked the license plate, not knowing that she would also find the man responsible for Jimmy's death.
So while we might think to have been misguided by Natalie's earlier (in watching order) nice bevahiour once her misusing of him is revealed, the actual story development if seen in chronological order draws a nicer or at least more ambiguous picture of her character.