If you go to the profiles of the Buried Lovers, you'll see it says 'Are they a love interest?' and then in some, such as Lily, the answer is 'No.' I do feel your pain, though, I did kind of want to pair up with her too.
This game was so much fun to play! I went through two scenarios so far, in one, Cardan ____ me and in one, I became Rian's girlfriend. I liked both endings and I'm going to check out the other two options :3