He lied. Should I block him or let it be?

Anonymous
When I met him, he told me he broke up with his girlfriend already. Because we like each other so we go out once a week and then we kissed and had sex. When I was with him his girlfriend always called him, like a thousand times a day and he said it was annoying that she calls. I feel strange, normally if it's already his ex, she shouldn't be like that. But he said he broke up, just his ex is too annoying blabla and she still tries.

Then, just now, I found out that the facebook profile of his "ex" changed into him and her lol. So I think he lied to me apparently, he made me into a third person and I even didn't know that.

Should I block him? Is he a person that can't be forgiven?
He lied. Should I block him or let it be?
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