Actually it won’t. Like u said, the doctor wants the family bloodline to continue but the duke doesn’t. It can’t continue unless it’s incest because nobody from house Taran can have kids unless it with each other (within the family) That’s why the duke and Lucia had a fight. They made the contract even when Lucia told him she couldn’t have kids. He didn’t care cause he knew that he wouldn’t be able to get her pregnant anyways. But now that he actually loves her and is actually willing to have a baby with her, he doesn’t wanna tell her about his family’s curse. That’s why Lucia was upset. She couldn’t understand why he al of the sudden seemed infatuated with her when he said earlier that he didn’t care about having kids. Does that make sense?
Let me add this. Yes, she made herself infertile (because of the chances she might marry to the other old baron, which she dreamed about.) But after she digest the antidote made by the male doctor, she can be pregnant. Which cannot be lead to something more tragic. The only fault she made was to not tell the female doctor what type of grass (vegies) she eaten. And I’m more worried about the dukes reaction about her future bearing.
Because if a child born between two person with blood of Tarans' they will have a SON, if one of them is not a Taran, they will have a DAUGHTER . To preserve their bloodline, the other members of Taran family have to marry to their family to produce a son, the others members have to marry a woman outside the family to have a daughter, then the son and the daughter will marry each other to produce another son and the cycle goes on

whats with the taran bloodline that the doc wants it to keep flowing? isnt it gonna flow even if it isnt incest? i forgot whats happening pls help