I'm going to put a girl in a bearhug after witnessing her spread lies about me to my whole team
How do you know she did that?
I eavesdropped. I know she is lying.
It's wrong to spread rumors like she did. But getting physical with her doesn't solve the problem, talk about it.
I think that if a person lies then they should be punished.
You're right that a person should be punished if they lie, but the consequences should be social ones, not physical ones. If you get physical with this girl, then she could report you to the police and you could be arrested. You should confront her in a manner that does not involve violence.