First, you are absolutely worthy of a man who does not lie to you or cheat on you. That should be a GIVEN, and it's actually the minimum. You are worth so much more than what he has shown you.
You have your whole life ahead of you. You are smart and successful. You are a catch, a prize. He is not worthy of you.
Please read up on the 180 in The Healing Library. Understand you cannot make him not lie. This is like trying to make an addict stop using. He has to want - really, really want - to stop. On his own. Otherwise, you are in danger of doing the codependency dance with a liar and a cheat who will continue this pattern.
Liars do not easily change, but if you think he is willing to change, your best bet is to do a hard 180 and see what he does. The 180 will give you distance to heal and to think about what you really want in a relationship. What are you dealbreakers? It's important to know them, be firm in them, and give real consequences for infractions. It's not easy, but you can absolutely do it.
Keep listening to your gut and note any red flags that come up. Write things down so you don't forget. It's all too easy to forget stuff when you're heart is on the line.
Gently, it may be hard to fathom right now, especially since you are afraid to lose him, but there are definite patterns in betrayal. Lying is a serious red flag and pattern. You don't have to decide right now, but do take the time to read up on the 180 as well as others' stories.
Gently, I do not like his "you'll do" attitude at all. He's comparing you to another woman and went behind your back. His "experiment" excuse is more than lame and highly suspect. The lying and the date alone show you this man's character and exactly what he will do in the future.
The burden is on HIM. He must do the hard work to win you back, and if he doesn't, you'll know.
If it helps, you can think of the 180 as your own "experiment" to see if this man is truly worthy of you.
While you are doing the 180, take excellent care of yourself. Self-care is huge and you need it now more than ever. Seek out your own IC, a good one, and gain some distance from this man while you process what has happened.
I dated and lived with a man who lied about little things. It was a baby red flag, so I brought it up each time I caught him in a 'little white lie'. It was so frustrating, why would he lie about such little things? We'd fight over it, and he'd finally admit to lying and promise not to do it again. I explained to him that it's not easy to trust someone with the big things in life if they constantly lie about little things. I thought it was a character quirk, so I eventually let some of the lies go. I figured it was likely due to FOO (family of origin) issues. I gave him the benefit of the doubt.
Fast forward 21 years later, and this liar turned out to be a cheater, too. Multiple affairs and a secret life. Had I known what I did not know then, I would have run as fast as I could. Nothing would have stopped me from leaving this man if only I had known what devastation marrying him would bring. We had a good life together. He was my best friend. I loved him dearly and was in the marriage 100%. None of that mattered. He was a chronic liar and, as it turns out, a cheater too. Double life. I honestly don't understand how anyone can do that, but it happens. I still can't wrap my mind around the things he has done.
You are the only one who can make this decision. It bears repeating - realize nothing you can do will change him. He has to WANT, really want, beyond anything, to change himself. If you give him no consequences for what he has done to you, why would he change? And why would you just take his word for it? He has to SHOW you beyond any doubt that he has changed. You must be witness to his changed ways in the present because future promises from a liar are worth zilch.
I'm so sorry, I know how difficult this is. It sucks beyond measure. None of us wanted to be here, and yet here we are. We can offer support, advice, feedback, our stories, what we've learned and how we've grown. We are here for you and each other.
You are obviously a caring, trusting, accomplished woman who deserve someone that gives you the BEST ODDS at a happy life. Do not settle for less.