Lapis is a miserable wreck of a being because she was trapped in a mirror for millennia, then suffered traumatic abuse shortly after.
Assumedly in this AU if Jasper/Peridot/Lapis are replacing the Crystal Gems as the outcasts on Earth watching over Steven, then Lapis will not have ever suffered everything which made her a miserable wreck. Who's to say she wouldn't be the happy-go-lucky one, before all that horrible shit happened to her.
Besides, you need at least one character that childish Steven can get along with on a similar wavelength, and it certainly isn't Jasper or Peridot. Not to mention the creator was clearly applying the same roles the Crystal Gems had in Steven's life, to J/P/L in a way more than the characters themselves actually are. Jasper in the video was actually more like Garnet than she is in the canon, Peridot was more like Pearl, and Lapis was more like Amethyst.