Lapis is her own judge, jury, and executioner. The pain in her expressions, the venom in her inner thoughts that is turned against herself, and her inner conflict specifically regarding Natori, are all incredibly visceral and get more pronounced the more light is shed on Lapis' inner workings. It's hard to read at times, but at the same time, the building and fleshing out of her character are incredibly satisfying.
Especially her inner conflict about Natori, and especially after the "reveal" that Natori has known all along. It's clear that Natori's words and kindness and other feelings reach Lapis, and I'd say are so, so close to breaking through her facade, but Lapis does everything in her power to reject it all, as well as her own feelings because in her mind there's no point. She's already doomed, there is no way back. Makes the romantic tension between the two so much more palpable and delicious.
...I do feel her and Gran will eventually help Natori...
Almost definitely, I believe. I read Diana as one who may have a competitive streak, but when all is said and done, when it matters, she puts even this aside. And as you said, she sincerely cares for Lapis as well, so I don't really think she'll get in the way of anything.
As an aside, the art in this series has been incredible from the beginning, but chapter 11's designs were phenomenal.