Employment Law Questions? Ask an Employment Lawyer.
I'm Lucy, and I'd be happy to answer your questions today. I'm sorry to hear about your situation.
There unfortunately aren't any general workplace bullying laws that require people to be pleasant to each other or stops someone from saying that they don't like each other. In order to have a cause of action, you'd have to be able to establish that he's making false statements (like claiming you're late frequently when you're not) OR you'd have to be able to allege a hostile work environment on the basis of your gender, race, religion, sexual orientation, or member as status of another protected class. Is there any reason at all to think that your supervisor's behavior is based on illegal discrimination?
If there isn't, then the only recourse is to talk to his supervisor or the HR Department so there's a report of his behavior, which lets them determine what action to take.