I presume you are referring to the scene in which he gives her a month to think about her decision. If that's the case, he had not yet fallen in love with her, but was using his professionalism to ensure that she was perfectly happy with the decision and it wasn't just a passing mood. I imagine even a hitman might feel pity for a girl that sees no other way to escape her misery, so he is not yet in love with her. Only when he thinks the decision over himself at home does he begin to feel pity and some sort of love. He invites her to lunch in Carmel so that he might try to persuade her to abandon her plans by showing her that life is still worth living. I hope that clears up that question.
"Interesting" might be one way of putting it