Dove beauty bar (original formulation) is not actual soap. It's a blend of synthetic detergents (syndets) with some soap. It's superfatted with fatty acids, not fats.
I honestly don't know of a way to adequately duplicate a syndet cleanser using only lye based soap, if for no other reason than the pH of syndet cleansers is usually acidic. There is no way lye-based soap can be acidic or even neutral (pH = 7).
If you want to replicate a Dove product, you'll need to look up the ingredients list of that product and formulate accordingly.
As far as Dove beauty bar feeling good on skin, I have to say "to each, their own". I really dislike using the Dove beauty bar for bathing. I'll use it only if there's no other option. Getting away from Dove was one of the motivations I had for learning how to make soap.