My daughter swears that my 100% lard soap helped her acne more than anything she's tried. It's just plain old lard, soaped at cool temps, 4% superfatting and fully gelled. But if I was going to add anything to it to improve on it, it would be tea tree and/or clay.
I LOVE clay soaps, and they are nice for oily skin. You don't want to scrub the skin... it just makes the problem worse by causing irritation, more inflamation and spreads infection to other pores. But clays don't scrub. They sort of draw the oil and funk from the skin, so it doesn't scratch the skin like exfoliating stuff does. Exfoliating is great for us old ladies and men, but not for young acne-prone skin.