lies are not illegal. if what the person says is illegal though, a publisher can be sued and face the same liability

What does this have to do with CNBC discontinuing Trump's press conference? Do you think he said something illegal?

No. I just answered your question and pointed out that there's a big difference in the legal protections offered to twitter. What twitter did is borderline ethical, it would have been more honest to ban trump rather than plaster his tweets with their own opinion of them.