Should I dump him because I suspect he has herpes?

So I've been talking to this guy and getting to know for the past several weeks.
Today he turned up with a cold sore on his lower lip. I asked what it was? He said it's a cold sore and it might be genetic because he said his mom gets it all the time.

I think he's lying and I suspect he has herpes. Should I make a run for it?
Should I dump him because I suspect he has herpes?
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