I wondered if Lars didn't fall in love per se with the doll, but rather the concept of having her as his girlfriend was a defense mechanism, kind of like a way to cope with the pressure he felt from his sister in law about having regular dinners at his brother's house, and also the pressure and contradicting emotions he felt from the interest shown by the girl in his office.
For most people, when confronted with the choice of starting a romantic relationship, contradictory feelings do surface. This might be magnified for Lars, given that he is (portrayed as) socially awkward.
The doll served as a buffer between him and the community he lives in. He was able to socialise. Perhaps he felt less intimidated and lonely when he has someone who he can talk to. Talking to an imaginary person/doll is more acceptable than talking to the air or to plants, it seems. It certainly garners a whole lot more understanding and compassion from people who see it as a desperate kind of loneliness.
Perhaps also, the doll was a trial phase for Lars. He did get to practise 'caring' for the doll and he did tentatively learn how to act around people as a couple. Viewed in this manner, he was being practical, and he had the advantage of being misunderstood/unfathomable yet accommodated simply because he was strange.