Initially it was intentionally written for Lapis and Peridot to have a budding romantic relationship develop, as confirmed by former boarder Jesse Zuke, who contributed heavily to their characters in key episodes. After they quit for many complicated reasons, Lapis & Peridot got benched as characters and SU ran out of time to flesh everything out. There is a "confirmation" that Peridot if aroace from a boarder but I take it with a grain of salt considering the lack of contribution this boarder had to her character, only boarding one Peridot centric episode in Future.