I think he's likely trying to scare you. If he really wanted to go after you for this, he wouldn't go to a lawyer. He would go to the police, fill out a report and tell them that he was fearful for his safety and wanted a protective order. The police would send him over to the DA's where one would bring him before the judge and get an order protecting him. You'd be charged with a crime -- probably not a terroristic threat as it's a bit much for this type of an offense, but for a harassment or an aggravated harrassment.
So what he's telling you isn't the way things are done in New York.
He could get a civil order, but that's in Family Court
and wouldn't involve an arrest or criminal record
at all. He wouldn't need a lawyer to ask for the order or to get a hearing.
What you should do right now is to cease all contact with him. Maybe it will blow over, but if it doesn't, you sure don't want to make any kind of written or oral record that could hurt you if he presses charges or summons you to family court. The less you have to do with him right now, the better, and the better the chance that he may just cool down.
If he actually does want to go after you legally, you'd be served with a summons and/or a protective order -- and he couldn't be the one to serve it. At that point, you would want to contact a lawyer.