The two are never seen interacting in-game or in other material. However, in official Danganronpa relationship charts, Leon states says the following about Byakuya: "The heir of a distinguished family! Cool!" Meanwhile, Byakuya describes Leon as "a difficult being to understand."
After Leon's execution, Byakuya has a slightly concerned expression, which is a contrast to his usually stoic expressions, although his reaction was still among the calmer ones. This is likely due to it being the first execution and he didn't expect it to be so brutal.
Due to the lack of canon content, the ship is left mostly up to interpretation. Many enjoy the concept of the two of them starting off butting heads, but coming to a resolve at one point or another for various reasons. It is also thought that they would balance each other out in a simple, yet perfect manner. While Leon is a much more go-with-the-flow type of person compared to Byakuya's rather strict mannerisms, they both share traits of competitiveness, drive, and determination. As romantic partners, Leon could teach Byakuya how to open up and become more sympathetic, and Byakuya would more than likely bring out a much more mature side of Leon.
There is also a theory that, had Leon lived longer, he may have confided in Byakuya about the troubles he was having with his talent. In Leon's third Free Time Event, he tells Makoto about his wishes to go back to his old baseball team, meaning that he is at somewhat of an impasse about his career choice. The reason as to why Leon would have gone to Byakuya is because Leon doesn't know what to do with his life, while Byakuya has had his life practically laid out before him, making him the prime candidate to give Leon advice.
- Class 78th refers to the ship between the two and the other students of Class 78th.