Severe regrets because I lied in my PhD application

I appreciate the question.

I think we can all agree that you should not have lied on your graduate application. It is to your credit that you recognize this. That said, as a frequent thesis advisor and the recent head of Graduate Studies in my department, I feel that the main victim of this lie is...you. If a student of mine told me they had done that, I would thank them for telling me, confirm that they should not have done it, make sure they understand that they must never falsify any academic documents again...and then get on with business.

Cutting the funding of a successful student for this kind of indiscretion that occurred before their arrival is, for me, just not a reasonable thing to do. It is an interesting thought experiment to wonder what percentage of the graduate students in my department had an undergraduate indiscretion as bad or worse than this. Rough guess: somewhere between one third and one half? It is all but impossible to know and also very subjective.

You have to deal with your bad behavior in the past. An unfortunate fact of the matter is that it is often not possible or not optimal to directly fix past bad behavior. That can be an unsettling thought -- for me too, by the way. Based on the sleepless nights you describe, I am really glad that you are talking to a therapist about this and figuring out what you can do indirectly to move on with your life.

Here's an idea: you say you are doing very well in the program. That's great. Is there some optional service task you could take on in the program (or the department or the school or the profession)? I think that could be beneficial, both in reality and in your own mind. That way, when you think about the bad thing you did two years ago, you can also think "Yeah, I feel bad about that, but I feel good about X that I am doing now." By the way, if you do it, you certainly should put it in your CV, but if (and only if) it seems helpful for you to be a bit modest/understated about it, you could pitch it that way.

Good luck.

Two things.

You are correct to talk to a personal counselor about this issue and your feelings.

Second, forget about the past as long as you don't need to lie again to go forward. If you are questioned about it, you should be honest and apologetic, but there is no need, really, to bring it up and complicate your life. If you have proven yourself worthy after a couple of years, the past will be held less against you even if it does become public.

Many people have things in their past that they are ashamed of. If they can learn to avoid past errors and also feel good about their own self-worth, they have made progress.

An alternative is to talk to a trusted faculty member about it and ask for advice. I don't think that it is essential to do this, but if there is someone in your circle who knows how you behave now and how hard you are working to improve, then such a person might be able to offer help and also to stand up for you if questions arise in the future.