@Ethyn2984,
1. Are there any agreed upon stipulations on your open relationship?
2. Are either of you allowed to have sex with other people without informing each other about those encounters?
If there are agreed upon stipulations or rules broken, that can very well be seen as cheating.
If there aren't any agreed upon stipulations or rules broken, then all is fair game.
In regard to her lying to you about having sex with him and other lies, that is a whole different issue. You might want to have a discussion with her about the lying to you. An open relationship doesn't necessarily give her the right to lie to you, unless that is what both of you want.