She's the only one with mystery to her at the moment. It seems we're still setting up a lot of things in this first volume, so I imagine we'll start getting deeper into Lapis soon. Each chapter teaches us more about Lapis, even when she's not physically there.
Here we learned that, like the prince, she apparently feels she is locked into a set path (possibly be birth) and that the prince has presumably tried to help her see another way. She mentioned something about this in an earlier chapter when she made a comment about playing her role (or something to that effect). We also learned, again, that Natori is in denial about her feelings for Lapis and that Lapis considers her "responsibility" like a game of "chess," that leaders should be willing to play and sacrifice for.
Right now her character is a bit more subtle and requires more reading between the lines and that's always going to be a harder sell initially compared to someone like Diana who is pretty upfront and mostly straightforward. This is good though because it means we have a lot of depth to get through between Lapis and Natori once the author starts in earnest. But this feels like setup for Lapis, and worldbuilding, before Lapis starts coming back into the focus more (physically at least).