Why is my ex boyfriend telling me that he fantasizes about me?

If he lies to you about everything, why would you continue talking to him?

People who lie need a clear cut message sent to them. If they are caught by a family member or friend, those people need to cut them off completely. Eventually that person will figure out that when they lie, the people around them disappear.

And in your position, you can do this perfectly without worrying about a family outing or scheduled event.

Don't worry about what he means or why he's doing this. You know him to be a lier, so he's at least playing some game.

Cut him off and move on.

It means he probably still has feelings for you and wants to get back together with you. He's hoping you will feel the say way back. Although, you said he kept lying about everything to you so I suppose there is a remote chance he's just screwing with you. But I would think the former is more likely than the latter.