It might sound surprising, but forgiveness as an intentional act is unnecessary to the success of rebuilding betrayed relationships. I have seen a great many damaged relationships completely repaired with no one saying, “I forgive you.” Forgiveness does not mean condoning or excusing bad behavior.
Can betrayal ever be forgiven?
Too often, people who have been betrayed in relationships appear to forgive, when they are simply giving in. They can't be bothered suffering anymore, and they'd rather go back to the way things were before. So they accept the apology offered by their lover, and agree to move on.
Should liars be forgiven?
If a person lies, and is unrepentant about it, you are under no obligation to forgive. If the liar is sorry, you still do not have to forgive. ... Even if the other person is genuinely sorry, some grave matters may not or should not be forgiven in the sense of "everything between us completely is all right again".