"Lamentations of June" is a surreal and philosophical story set on June 30, 1974, in Paris, France. The narrative follows June, a 27-year-old woman with a pixie haircut and blue overalls, who has a "sixth-sense" that allows her to have visions about other people's lives. It is unclear if the characters she encounters are real or imaginary.

June sits at a bus stop and interacts with a series of intriguing characters. She first meets a man who is overly forward with her. She tells him to go away after a passionate kiss, as she knows "nothing will come of it" due to her clairvoyance5555. She then meets a young woman, on her way to an audition, and foresees her future as a "tremendously famous" actress named Giselle.

Next, June encounters an older woman, a self-proclaimed communist who works at the Eiffel Tower selling tickets. The older woman shares a harrowing story about surviving World War II by sacrificing herself to German soldiers, a choice she insists was not important because it saved her eleven companions.

Finally, a man named Dr. Weinstein, described as balding and "quite dapper," arrives and reveals that June is a case study in his new book on phenomenology. June realizes that his book's success will expose her to the public. Prompted by a "sensation" she should leave France, June decides to go to America, possibly Quebec, to escape the coming publicity. The episode ends with June walking away from Dr. Weinstein, ready to begin a new journey.