I think this question has more to do with why a person with a lot of fast-twitch muscle types have higher stamina. Especially if you pair it with this question.
First, there are actually three types of muscle fibers. Type 1 (slow-twitch), type 2a (fast-twitch), and Type 2b (super-fast-twitch. Also called Type 2x). Type 2a is kind of an in between between Type 1 and Type 2b. (There's also a Type 2a/2x but that's not really important for the question).
While this doesn't have anything to do with Lebron James or basketball specifically, there was a study that compared muscle fiber types of Olympic Weightlifters. They studied 21 athletes that combined were in
3 Olympic Games, 19 World Championships, 11 Pan American Championships, 49 National Championships, 32 American Opens, 8 University National Championships, and 25 Junior World/Pan American/National Championships. Participants also held 25 national records and >170 national/international medals either at the time of the study or in the past.
So these were top-tier athletes.
What they found was their muscle composition was around 23% Type 1, 67% Type 2a, and 6% Type 2b.
So, the takeaway as it's related to this question is that athletes don't just train a single muscle fiber type. They train all muscle fiber types with an emphasis on a particular one. If weightlifters didn't train slow-twitch muscle fibers, then the percentages would be closer to 0% as the Type 2 overtook.
Specifically for basketball players like LeBron James, they run fast, but they're not sprinting at full speed every second of the game. They play basketball for many hours a day in addition to any sort of supplemental drills and training they do outside of basketball. That is going to train far more Type 1 and Type 2a muscle fibers which are necessary to perform for very long durations.