Ex trying to contact me. I need Advice

My ex and ended back in April and it was a really bad ending. I found out he was talking to other girls. And when her and I both confronted him he decided to get back at me by telling my parents him and I were sneaking around together since my sophomore year ( I just graduated so 2 years) and he told my parents that we had slept together. Out of the blue I get a notification saying he added me back on Snapchat. He hasn’t yet messaged me but I feel like he will soon and if he does I don’t know how I should handle it. If anyone has any advice please give it

I don’t want to just block him for the simple reason if he try’s to contact me I would like to know. I just need advice on how to handle it if he does