One common theme is friendship. Since they are both characters, their relationship as friends is often explored. Another theme could be redemption, perhaps one of them has made a mistake and the other helps them through it.
One common theme might be the exploration of their relationship dynamics. Since they are two distinct characters, fanfic might focus on how they interact and get to know each other better. Another theme could be adventure, where they go on some sort of journey together.
The plot could involve Lapis and Peridot fusing accidentally at first. Maybe they are trying to work together on a project, like building a new structure for the Crystal Gems' base. Their powers interact in an unexpected way and they fuse. Then, they have to figure out how to function as this new being while also dealing with the reactions of the other Gems.
One possible fanfiction could be about Lapis and Peridot fusing during a time of great danger on Earth. They fuse to protect their friends and the planet from a new, powerful enemy. Their combined powers create a unique and beautiful form that has abilities neither of them had alone.
Some dedicated Steven Universe fan communities might have fanfiction archives or threads dedicated to this pairing with the hurt/comfort genre. For example, certain Discord servers focused on Steven Universe fandom. Members often share and discuss their favorite fan works, and it's possible to find some great Lapis Lazuli x Peridot hurt/comfort fanfics there. You just need to join these communities and start exploring.
Sure. You can try searching on popular fanfic websites like Archive of Our Own. There are often many creative works about lapis lazuli and peridot pairings there. Just use the search function and type in 'lapis lazuli x peridot' to find relevant fanfics.
A good one often has a believable scenario where either Lapis or Peridot is hurt, either physically or emotionally. For example, Lapis might be dealing with past traumas from her time trapped in the mirror, and Peridot is there to comfort her. The characterizations should be on - point, so they act like they do in the show.
Finding "peridot x lapis lemon fanfic" can be a bit tricky. Some fanfic communities on social media platforms might be a good place to start. You can ask fellow fans if they know of any good ones. Also, make sure to respect the rules and guidelines of each platform when looking for fanfic, especially if it involves certain pairings.
Since the concept of 'abuses' is not family - friendly in itself, it's very unlikely to find such fanfictions that are also family - friendly. Fanfiction should be a medium to tell positive stories, especially when it comes to characters that are often loved by a family - friendly audience like those from Steven Universe. So, I would say no.