Lol here is a little spoiler summery
from my understanding his twin brother and his sister who was in jail(?) had a child bu they died. The doctor dude, Philip, is obsessed with this family and is his sole goal that they continue the bloodline. He will secretly give mc the antidote so she can have a daughter. His plan is to make the daughter and the son have children together, basically more incest. This is what I got from other spoilers from the comments, if you want to know more just read the comments, some of them read the novel and understand the story more than I do. Here’s the Nobel, I encourage you to read it since it’s way more detail and the sexy scenes are much detailed. https://www.novelupdates.com/series/lucia/
Didn’t the duke have a son ?