In the nez Bat Man movie exactly what was the cause for the jokers cut lips?

In my opinion, the whole point of that was to show how manipulative he was. He acted as if he was trying to get people to sympathize with him, but there was no real reason to feel pity when he kept changing his story. It was all an act and we never got to know the underlying cause of his bizarre behavior, but that was part of the movie's message. He didn't have to have a good reason. As Alfred said, "Some people just want to see the world burn."

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Yes, I don't think either story was supposed to be true. He didn't want anyone to know the truth. He just wanted to keep people off balance.

The comic The Killing Joke has him down as an unreliable narrator, so no one can say what the real cause is. In the Lovers & Madmen story arc it was Batman himself who did it.
As for the film, if they even make a next one, it won't be Joker-centric. I think it's safe to say they're done with him.

I don't know.

He made those scars himself. Self-mutilation. He gave different reasons for the scars, because he wanted to be mysterious. He did want anyone to be able to put a finger on him.