Forked tongues are something that snakes (usually) have.
Also, in the beginning, Satan snuck up to Eve in the form of a snake, getting her to eat the fruit (and in turn Adam), which cast them both out of the Garden of Eden.
(Whether you believe in the Bible or not, most English-speaking people know this story, or think of Satan as having a forked tongue.)
So you also see forked tongues on demons and monsters, and you would say liars (because Satan is the king of lies) also have forked tongues.
I’ve never heard about a cheater having a forked tongue, though. That’s different.
Another English thing about liars: “Liar, liar, pants-on-fire!” is a common kid’s insult/phrase to other kids who lie, so you might also hear about someone’s “pants being on fire” or “getting a little hot”… and that also has to do with lying.