Soap is an alkali (like sodium hydroxide or potassium hydroxide) combined with fats. So, by the very definition of “soap”, you cannot have soap without lye. That is like trying to make a baking soda and vinegar volcano without the vinegar. No vinegar and you’ve just got a pile of baking soda. No lye, and you’ve just got a bucket of fat.
It is important to use very precise amounts of lye, butters and oils in order to completely neutralize the lye and create a luxurious lathering soap that will moisturize the skin. We pride ourselves in having this calculation mastered and have never had any issues with the lye still being active in the soap.
The only way you can get a soap like product without using lye is to add a surfactant like sodium lauryl sulfate to water. Surfactants create lather, so you’re basically just getting lathery water that will act as an industrial strength detergent. As mentioned, a lot of surfactants can be irritating and so strong that they are very drying to the hair and skin. This is the super cheap way big companies go about creating shampoo, dish soap, and other liquid soap-type things in our lives. These concoctions are not true soap, but since they’re mostly water, chemicals, and petroleum byproducts, they sure are cheap.
