hii Yona thanks for the comment again!
About the lamb..
MAJOR SPOILERS BELOW
Yepp, the Lamb was intentionally trying to meet the Wolf. It's implied that he comes from a well-off background (his clothing, lack of awareness, etc.), which is why the MC assumes he's sheltered and unaware of the danger around him.
He knew about the serial killer because the Wolf was already well-known in the area for only targeting young (and attractive) men. While no one actually knows whether the murders were committed by the same person or multiple, the townspeople and the newspapers began referring to the killer as "The Wolf", an umbrella term.
It isn't explicitly explained through the MC's limited interactions with the Lamb, but based on his bad ending you can infer that he's unhealthily obsessed with the idea of the serial killer/the Wolf, to the point of leaving behind victims or even trying to seek the Wolf out himself.
To increase the chances of meeting the Wolf, he deliberately acts like the "perfect victim" (spraining his leg, keeping up an innocent act, etc.).
The logic behind the good and bad endings in the Lamb's route is determined by how much the MC is also "acting". For example, if the MC tells the Lamb they're gathering herbs instead of claiming to be lost, he'll be more inclined to believe the MC is the Wolf later on.
Despite being a wolf dressed in sheep’s clothing, the Lamb is just a naive young man who's obsessed with the idea of the Wolf.
That's why if the MC really was another victim lost in the woods, then he had no reason to doubt it (if you chose to lie). But if the MC was the Wolf, then he wouldn't care whether what MC said was true or not, since he found what he was looking for. So the choices in the Lamb's route were just about convincing him you were the Wolf before finally admitting it at the end
thank youu ♡