When one partner has been betrayed, they usually ask their spouse the wrong question: "Did you have sex with that person?" Emotional infidelity is far more damaging to a relationship than sexual infidelity. Open gay relationships can work, providing there are rules and the rules are followed. Lies are the ultimate betrayal in a relationship.
Lying undermines authentic communication and the offended party then has difficulty trusting anything their partner says. Lies designed to protect the third person in a triangle are particularly damaging because the liar has put his own interests and the interest of the liaison partner ahead of the interests of the spouse. Loyalty has shifted.
When words can't be trusted, only changes in behavior can begin to restore trust—and that takes a very long time.