Diana will lose Natori because she simply wants to protect Natori.
Lapis wants Natori to grow and to become a proper individual. She will protect her if she needs to but I think she's wanting Natori to be her own person. Natori, in theory, will eventually recognize that (as well as the fact that Lapis makes her heart race and that she, herself, wants Lapis to change and grow because she loves her).
It's not enough to want to treasure someone you love, which is what Diana wants currently, one has to be willing to encourage and push your beloved to better heights.