I'm not going to respond to a team lead's chats. Is that rude of me?
That depends on why you're ignoring them.
He has got in the way of my life way too frequently in the past.
If he's actively interfering in your life, then it's fine to ignore his chats.  I assume they're not super important or anything?
Maybe after I've chilled out a bit I will come back and chat.
I think you're making a rational choice. It's okay to spot when you should or shouldn't do something, like responding.