No one likes being lied to, which is why you must never tolerate a lying partner. All people lie to a certain degree. Some of these lies can be minor, which are called "white lies," but if your partner lies about big things (like for example if he or she is living a double life) that is simply unforgivable. You need to know that the more a person lies to you, the more these lies are going to escalate in the future, meaning they are going to become about bigger things.
You need to have a talk with your partner (if he or she is of the lying kind) and tell them point blank that if they continue with their behavior, that you are simply going to leave the relationship. Do not give them second or third chances, as that is only going to cost you in the end.