Lila first posed as a love interest in the episode Arnold & Lila where Helga wrote that Arnold loves Lila on a wall (to cover up that she originally wrote Arnold loves Helga). When Lila reads this, she believed it to be true, and decided that they should spend every minute they could together. Arnold is confused by Lila, as he says, he likes her, but does not "like her like her". When Arnold eventually breaks up with Lila, he thinks about the time they spent together, and realizes he actually does have feelings for her. He tells this to Lila, but Lila rejects him, telling him that after being rejected by him, she realized that she doesn't like him like him anymore. This crushed Arnold, but he doesn't give up.
For a good part of the remainder of the show, Arnold tries to get Lila to like him like him, but to no success, many times due to Helga who thinks of Lila as an enemy since Arnold likes him. She even refuses to go to a movie with him, because that might show that they are in a relationship. However, in the episode, Love and Cheese, when Arnold takes Lila to a carnival, and after Arnold saves her (while Helga tries to sabatoge their potential relationship) Lila says that now she really likes him, but still does not like him like him.
In the episode Timberly Loves Arnold, after being rejected by Lila another time, Arnold decides that he and Lila were just never meant to be, and gives up on trying to get her to like him more than a friend.