Oh I know this! It’s a spoiler from the novel, so DO NOT READ UNLESS YOU WANT TO BE SPOILED!!!!!
First, the baron is infertile. In the past (like childhood past) our lady had her first period. Obviously because of no one being there for her, she did not know it was normal and thought she was going to die from excessive bleeding. So she ate a herb that is suppose to stop bleeding. She continued to it, until she no longer had her periods at all even as an adult. So in a sense, she is infertile.
They will have a baby.
Lucia's infertility is actually one of the conditions needed in order to bear a child with the duke. Taran's family doctor has the cure for Lucia's infertility, but lucia also knows the ingredients for it from her past life. So once they have decided to have a baby, lucia just needs to drink the medicine to be fertile again.
As the previous comment said, they will have babies. Because of the ML family lineage, there is a very specific way of having babies. And it so happens from the blessings of our author, Lucia already accomplished step one without her knowledge. I will not go into too much specific details since I feel this is almost the foundation of the story itself. But do know that yes the couple does get a biological baby, and yes this entire process of getting a baby is very hard and the entire story nearly wraps around it.

Ba-bump, Ba-bump, Ba-bump
O-O What roundness be this?
heheheh this means the 'ol baron was the infertile one and not our lovely lady...i kinda wonder how that didn't cross her mind that may he was the problem and not her......