So, regarding the original timeline.
I guess that original Welhelm also did something similar with Lisbeth like the reincarnated one did.
Except, he did it much later, and either kept lying until original Rudolph was killed, or somehow found the truth about the connection between Lisbeth & Rudolph and either stole the coin from Rudolph, or claimed that it was Rudolph who stole the coin from him.
As for original Rudolph, he probably learned that Lisbeth was the girl he met, and felt cheated & betrayed when she went to Welhelm, which might be the last line that eventually made Rudolph cross the line and become the Tyrant King. And because of misunderstanding that Welhelm created, Lisbeth ends up eventually killing Rudolph.
Or else, the whole story about original Rudolph being a Tyrant King was false to begin with.
It's possible that original Welhelm was the one who was the Tyrant King and stole Lisbeth from MC, and after killing him off, started to rewrite history with his own narrative of Rudolph being the Tyrant King, so that future generations would praise him as a Hero, while his bloodline remained at the highest position.
On another topic, really find it odd that people call a child/kid as Tyrant Prince because he was being a brat and feared him, but still didn't let a chance go to bully him.
I mean, if he is a Tyrant and a Prince (even if an illegitimate one), then people lower than his position should be fearful of him, not bully him.