turns out back then Lisbeth was visiting the palace with her father the duke. While the duke was busy talking with the emperor she went to play in the garden however she went too far inside and got lost. There she met Robin and two men who chased her away claiming she doesn't belong there.
Lisbeth was scared but then she met a boy with golden eyes (and golden hair however she forgot about the hair years later). He was Rudolph (except she never got his name and viceversa). So he played with her and asked her where she was going. She told him and so Rudolph took her to the first queen's garden. They spent some time there talking when someone approached, it was Robin and his goons.
Rudolph hid Lisbeth behind the flowers and faced Robin, as a result he was insulted, beated down by his goons and mocked by Robin. Lis was scared and could only see them abusing Rudolph then they lost interest and went away. She hurriedly ran out to check on him however prince Rudolph instead reassured her and asked if she was okay.
They chatted for a while but Lisbeth wanted to do something for him, however she didn't have anything to give as thanks for saving her from prince Robin and his men. Then she remembered she carries an old rare coin with her, one every member of her family exclusively carries with them from generations to generations. So she took it out and gave it to Rudolph, telling him to never give up and she would see him soon in the future. He was reluctant at first but gladly accepted it. Afterwards he helped her find her way to her father and promised to see each other again.
Fast forward several years close to the present. Wilhelm, the son of a branch family to the royals from long ago (his grandfather was cousin or brother to a king from past generations) showed up at one of those gatherings/parties of noble children in front of Lisbeth. He was overly familiar with her claiming he was the child from back then in her memory. He speaks of the time he saved her from Robin and showed her to the garden and the promise they made to meet again.
Lisbeth was happy at first but being cautious she asked several questions, many of which Wilhelm avoided answering. He has golden eyes, sure but she felt something weird in her chest. So he kept on courting her for several months, pestering her even when she was at home. At first she allowed him to visit her but soon she felt weird around him because she asked about the promise and the "item" she gave him back then. After many months asking him, he finally claimed it was a "brooch" and that made her feel sick and suspect.
She sent many of her maids/spies investigate Wilhelm's past. Meanwhile she received an engagement proposal from prince Rudolph. They met and he told her many things to scare her, like talking crap about him being a narcissist to him being constantly bullied and becoming a target of assassination attempts. Lisbeth suspected him being the boy from her memories and not Wilhelm but what sealed the deal was Rudolph dropping the coin in front of her. It was just a second and he hurriedly pick it up but she noticed the peculiar old coin. She accepted the engagement and left.
Now here is the deal, you need to understand all this before the actual explanation: back then when Lisbeth was found by Rudolph, Wilhelm was visiting the palace. From young age he was told the king from the past took the throne from his ancestor grandfather. So Wilhelm ended up in a poorer household and he was blamed by his father for some reason.
Wilhelm is a pos since childhood you see, he is envious of others like the royal family. So he witnessed Rudolph and Lisbeth meeting. At first he was amused by the two "idiots" being chased away by others, but then he thought Rudolph had "everything he didn't" and that pissed him off. Then Robin and his goons appeared and he saw Rudolph protecting Lis and their promise afterwards HOWEVER because of his position he couldn't see what she gave him (see, this is why he didn't want to answer and only made up "a brooch" later on).
So when they left Wilhelm thought, wouldn't it be good if he could make this prince Rudolph miserable? By chance me met several years later Lisbeth in a gathering, she wasn't the brat he remembered but a beautiful girl and an idea sparked in his mind. Something cruel like make her believe he was the boy who saved her. He would not only have such beautiful girl for her own but also the power of the duke's military family. Then he started pestering her.
So. This leads Rudolph to speculate way ahead in the story:
a. Wilhelm actually fooled Lisbeth in the "other timeline" and made her kill the mad emperor Rudolph.
b. It was never a mad emperor Rudolph and Wilhelm made others rewrite history books after Rudolph's death.
c. Possibly even Lisbeth died and couldn't tell the true story then.
In all cases Wilhelm survived and ended up being a hero figure for the new empire.