I'm Going to Become the Dark Duke's Family

I’ve been reincarnated into a book, and I’m dying. I have the same terminal illness as the heroine, but in the original story, I’m dead long before the cure is ever found. To survive, I have to snap the villain out of his downward spiral and force him to find the medicine early. “Hello, Your Grace. I’m Lowena Wheatfield, I’m ten, and I’m from the Townsend Orphanage.” “……What?” “Adopt me. If you do, I’ll greet you at the door every day. And, if you’re lucky…” “What else?” “I’ll even give you a goodnight kiss.” That’s settled. I’m joining the villain’s family.