Dude, walk on. That bad behavior is too egregious to tolerate.
Were it me, I wouldn't even bother trying to find out the extent of the lying, nor would I care why it happened.
The single greatest lie I see is the one where she claims to love you. There's no love or respect involved in behavior of that sort.
The notion that anything can be worked out or that you should make an attempt to work it out is so much nonsense. Nobody should tolerate behavior of that sort from anybody else. It is not a virtue to put up with that and try to work things out--it is dysfunctional.
When speaking of various forms of non-monogamy...it ain't poly if you're just fucking around.
While polyamory, open relationships, and swinging are all distinctly different approaches to non-monogamy, they are not mutually exlusive. Folks can, and some do, engage in more than one of them at a time--and it's all good.