Will regret be part of the torment of hell?
Yes. Constant regret will be part and parcel of the torment of eternal doom—the realization that they are there and did not have to be. They will recognize they made their own choice for it, even though God made escape possible through the finished work of the cross.
Les teaches that hell is a place of eternal, bodily torment experienced with all senses and feelings. He explains that as awful as it is, those who go there will realize they made their choice for it. Even those who seem never to have heard are without excuse. This constant regret—that they are there and did not have to be—is part and parcel of the torment of that eternal doom. God is absolutely just and fair, and through the finished work of the cross He has made escape possible for every human being.