I disagree. He originally told the lie about sapphires to protect her from being raped, since he gained a bit of respect for her as a fighter (as a man, so to speak), and he was content to leave her behind until he learned that she would be killed because Bolton's lackey expected sapphires.
If you're trying to say that he was motivated by her relationship with Catelyn, I'd be interested to hear your reasoning. Otherwise, I'm not sure what you mean. My perspective might also be biased by the fact that I have read the books, and I do know what happens next.