Although the idea of lye in soap gives some people pause, the lye is completely nutrilized in properly made soap, leaving the fat the moisturize your skin.
In my experience, the most ancient of chemical combinations (lye with solid and liquid fats) create the most cleansing soaps. The current glycerine based chemical soaps do not have the same properties of bonding with the oil based particles. This explains it pretty well:
How does Soap Work?
Nearly all compounds fall into one of two categories: hydrophilic ('water-loving') and hydrophobic ('water-hating'). Water and anything that will mix with water are hydrophilic. Oil and anything that will mix with oil are hydrophobic. When water and oil are mixed they separate. Hydrophilic and hydrophobic compounds just don't mix.
The cleansing action of soap is determined by its polar and non-polar structures in conjunction with an application of solubility principles. The long hydrocarbon chain is non-polar and hydrophobic (repelled by water). The "salt" end of the soap molecule is ionic and hydrophilic (water soluble).
When grease or oil (non-polar hydrocarbons) are mixed with a soap-water solution, the soap molecules work as a bridge between polar water molecules and non-polar oil molecules. Since soap molecules have both properties of non-polar and polar molecules the soap can act as an emulsifier. An emulsifier is capable of dispersing one liquid into another immiscible liquid. This means that while oil (which attracts dirt) doesn't naturally mix with water, soap can suspend oil/dirt in such a way that it can be removed. The soap will form micelles (see below) and trap the fats within the micelle. Since the micelle is soluble in water, it can easily be washed away.
from the website: Edinformatics.com