The Simpson family visit Story Town Village, an amusement park for babies, as a special treat for Maggie. In the village, there is a petting zoo, where Lisa is enraptured by a cute lamb. That night, Marge serves lamb chops for dinner, but Lisa is troubled by the connection between the dish and its living counterpart, and announces that she will no longer eat meat. In response, Bart and Homer mock her relentlessly. Reaction at school is no better; when Lisa requests a vegetarian alternative to the cafeteria food, Principal Skinner labels her an "agitator". The students are then forced to watch a Meat Council propaganda film, "The Meat Council Presents Meat and You: Partners in Patriotism", starring Troy McClure, which portrays eating meat as a patriotic duty, and criticizes vegetarianism. Lisa is unimpressed by the film, but her classmates tease her.
Homer and Bart continue to give Lisa a hard time at home, particularly since Homer is preparing to host a barbecue, complete with roast pig. Bart and Homer even form a conga line and sing, "You don't win friends with salad!" On the day of the barbecue, Lisa makes gazpacho for all the guests as an alternative to meat, but the partygoers laugh in her face. Enraged and deeply hurt, she climbs aboard a riding mower and drives away with the roast pig in tow. Homer and Bart chase her, but she pushes the pig off a slope and they are too late. The pig rolls through bushes, into a river, and is shot into the air by a dam spillway's suction.
At home, Homer scolds Lisa for ruining his party and demands an apology, but Lisa refuses to apologize and scolds him back for serving a meat-based dish. They fight and she leaves the house, not wanting to live in a house with a "prehistoric carnivore." As Lisa walks along, she decides that she can no longer fight the pressure to eat meat, prompting her to grab a hot dog from the grill at the Kwik-E-Mart and take a bite. However, Apu, himself a vegan, reveals that she has eaten a tofu dog, which he subtly switched out and none of his loyal customers had noticed the change.
Apu takes Lisa through a secret passageway hidden behind the cooler section assigned to non-alcoholic beer leading to the Kwik-E-Mart roof where they meet Paul and Linda McCartney. The McCartneys explain that they are old friends of Apu from Paul's days in India, and discuss their interest in animal rights. After a brief discussion, Apu asks Lisa what happened at home that made her upset. She reveals everything and while he understands, Apu warns Lisa that badgering others to accept her views can do a lot more harm than help. She is committed once more to vegetarianism, but realizes that she should tolerate those who disagree with her views.
Inspired, Lisa begins to return home and finds Homer frantically searching for her. Homer apologizes for his behavior, but Lisa admits she was wrong as well. She apologizes to Homer, admitting she had no right to ruin his barbecue; he forgives her and offers her a "veggie back" ride home. The final credits play over the still airborne roast pig.