"Homer and Lisa Exchange Cross Words" is the sixth episode of Season 20.
Lisa discovers she has an impressive knack for solving crossword puzzles and enters a citywide crossword tournament, but her feelings are hurt when Homer bets against Lisa in the championship match.
Bart and Lisa sell lemonade but no one comes so Bart places a dollar bill in the jar and people come to purchase lemonade from them. Homer then comes home from walking the dog and asks Bart for a glass which was to be put on his tab. Bart refuses, making Homer need to go to Moe's but needed to borrow Lisa's bike because his car was not working. At Moe's Tavern he sees Mrs. Krabappel trying to break up with Skinner, but can't so she offers a beer to whoever who could do it for her. Homer takes her up on the offer breaking her up with Skinner and with Carl commenting that Skinner felt better after the breakup. Lenny then asks Homer to separate himself and his girlfriend, Dorin, to whom was referred by Moe as having cheated on Carl with everyone except himself. Homer then does this but starts off the conversation by saying that Lenny is dead but then changes this when Dorin sees through his lie.
Lisa and Bart's lemonade stand is soon destroyed by the Blue-Haired Lawyer due to their lack of a vendor license. Bart then tries to bribe him with 35 cents but does so in vain. Bart and Lisa then go to get a vendor license but the man there is doing a crossword so Lisa plans to complete it for him and tells him to give everyone licenses.
Grady then asks Homer to help him break up from his boyfriend Julio. Lisa becomes obsessed with crossword puzzles after she helped the man finish one at the vendors license. Homer then goes to a hardcore gay club and breaks up Julio and Grady's relationship before breaking up everyone else's affair in the club's flirtation. Homer then breaks up the relationship of Ms. Hoover and an unnamed man, another man who was looking to get married and Snake and Grady.
Then after talking to superintendent Chalmers, Lisa enters a crossword competition and begins winning rapidly. Meanwhile, Homer under the advice of Marge and after a nightmare being chased by antique furniture, ghosts of people he broke up and the ghost of unborn babies stops his breakup business. He then finds a pub where the competition is being held and bets all of his money on his daughter using the money he got from the breakup business charging everyone 100 dollars. In the last match, he bets against her and wins because Gil Gunderson tricks her into picking up his glasses, stalling her so that he can win. Later, Lisa finds out that Homer is betting on her, and she becomes ticked off with him, disowns him and changes her last name to Marge's maiden name, Bouvier. Homer, feeling bad, and trying to get Lisa to forgive him, gathers the crossword editors of The New York Times, Shortz and Merl Reagle to make an issue, with a message on the diagonal grid from right to left and another reading to first letter of each clue. Lisa then forgives and hugs Homer.