Spoiler
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The duke didn't know about him. Only duke's father knew. Lapel's father aka Iorn (current duke's older brother) had an one night with an illegitimate daughter of a baron. He never looked for her again. The girl got pregnant and got expelled from her family. She then went to look for Iorn but she met the former duke and sensed something strange so she left. After that, she became a seamstress and was raising the kid on her own. She used to always move with her son not to get discovered by the former duke. She used to speak fondly of Iorn to her son. Oneday when she was drunk, she sent a letter to Iorn stating their son misses him but it ended up in the hand of the former Duke. And he sent his knights to kill her and her son. A knight took pity on the son and spared him. The former duke also made it seem like it was Iorn's order. When the son was 15, oneday he saw father with his wife and Lapel. He was furious as his father was very content with his family and so he started to plot revenge. So, nobody knew of his existence except the former duke.
Tbh, I don’t really think he’s at fault here. One nights stands are one nights stands for a reason. Who checks on that? Even in real life? Unless he manipulated her that they are gonna be something more, saying he had a fault in it is reaching hard. Why would he check her if they have no relationship with each other? It’s not like he would know she was pregnant if she didn’t tell him, unless it was specifically stated how exactly their sex went (aka if he came in her etc). I think blaming him is quite absurd.
I do understand your point,but he's also at fault. Even ml acknowledge his brother's fault. He blamed his brother for the happenings that terrorize their lives. The woman who Lorn had spent a one night stand was described as a good woman and mother. Although she's only an illegitimate child of a baron,she did not used her child to raise in power. She worked hard to raise him. She once wants to tell Lorn about their child but even that had almost cause her life. Lorn took advantage of her naivety. He did not used contraceptives,he used the woman to ease the heat. At least checking her would do. He should have thought that he might get the woman pregnant with his seed.
At first,the half brother did not want revenge but after seeing his father with another woman while being happy,his anger arose. You can understand him somehow,he and his mother lived in hiding and they strive to survive while his father is happier than ever,right? But he should have stop when his father and Lapel's mother died, because like him,Lapel is innocent and has nothing to do with their father's sin.
I know who wants to assassinate the child,and I really hate him for doing such a thing. He successfully killed the child's parents, killing Lapel won't bring him any justice. Anyways,it was ml's father's fault why Lapel was in danger. His brother,Lapel's father was also the reason why Lapel was targeted by that person.