making-friendos answered:

Ooh, a fun question! Well, after the events of Barn Mates/Hit The Diamond I imagine it was a combination of Peridot being a) hilarious and b) surprisingly empathetic that got Lapis to like her so much. I mean, we see later on that she’s pretty sensitive about Lapis’ triggers (i.e. Jasper), she must have let Lapis vent to her about some of the stuff that was on her mind.

Not the most original headcanon, but there ya go.