I would go to court. Fight it. Explain that you have a difficult neighbor, with a chip on his shoulder. If he doesn't have video, can't prove it, unless he tries to bring someone with him and say he had a witness. They, you get to dispute the testimony and indicate his witness is lying. In my State, if it's a traffic ticket, and an officer doesn't appear in court with you, the ticket is dropped. So, perhaps your neighbor might not even appear in court to lie.
Getting a lawyer for this would be like getting a lawyer for a traffic ticket.