If you pass a lie detector test, he'll just want you to take another one, or truth serum or something else to raise the ante. He's trying to control you and no matter how much you give in, it will never be enough.
You can end this relationship if you really want to. Break up, walk away, don't take his calls. If he threatens you, call the police, get a restraining order, get yourself free.
No one deserves to be treated as you're being treated, even if you did tell some lies two years ago, before you were a couple. This man is not worthy of you.
If you can't believe that, then please -- please please please -- find a therapist to help you, call a domestic abuse hotline or the toll-free National Domestic Abuse Hotline at 1-800-799-7233. Confidentiality is respected. They know what resources are available in your local area and they can advise you on the best way to get away while keeping yourself safe.
You are being systematically emotionally abused. It wears a person down to the point where you even think you need his permission to end the relationship. Please reach out for help today. You are not his property and you don't need his permission to leave him. You don't deserve this mistreatment.