I think this would be easier to explain in text, than in images, because their breakup is INCREDIBLY storied.
Back when Lapis and Peridot were together, Jasper was just beginning to assimilate with the humans on a more intimate basis. She didn’t quite by an apartment or land her job as a gym trainer, but she was beginning to engage humans more intimately. While Lapis was happy keeping herself, Jasper and the other gems separated from the Earthlings, Jasper’s interest began to inspire Peridot to venture out more as well. Lapis, on the other hand, didn’t want to do anything with the humans past an occasional “hello”. Everything changed severely when Jasper began dating Clara, Peridot herself was interested in dating humans as well, the way Clara and Jasper held each other made her more than curious for those feelings. She started hanging around Jasper and Clara more when she noticed that Clara’s punk-rocker friend, Amelia didn’t have anyone with her. After an encounter with her, Peridot quickly began changing her look and aesthetic to appeal to Amelia more, smoking, wearing leather jackets, chains and studs, and building up a profane vocabulary. While this was all happening, Lapis refused to change, or assimilate with the humans, creating resentment between the two, Peridot would stay out late with Vidalia and co, going to concerts and house parties, while Lapis waited around for her girlfriend to come home. By the time they were on their way out, Peridot and Lapis barely talked, until Lapis finally decided to try to win Peridot back in a last ditch effort by also changing her aesthetics to fit goth fashion, hoping Peridot would gravitate to her new look; she didn’t. A week later, Peridot moved out of their place and moved in with Vidalia in her winnebago/trailer, leaving Lapis behind. She never got over that rejection and still sobs at night, hoping that Peridot would come back to her–
All byproducts of Lapis refusing to change.