The "thirteenth step" is an aptly-titled extra "step" for the twelve-step recovery process, which dictates that someone, usually a man who is a veteran Alcoholics Anonymous member, must not start making romantic advances on another person who had just entered Alcoholics Anonymous. It is also a term referring to the fulfillment of only the first step (admitting that one was powerless over alcohol) and the twelfth step (having a spiritual awakening after completing the entire process and then sharing it with other alcoholics), while ignoring the other steps.
A promo for the episode is accompanied with the narration: "They're young. They're in love. And...they're killers." This is extremely similar (almost word to word) to a tagline for the film Natural Born Killers, which this episode is based from: "They're young. They're in love. And they kill people."