I wish there was such a thing as a completely natural soap made only from coconut oil, olive oil, essential oils etc. But this is unfortunately impossible. There is absolutely no way to make a bar soap without using lye.
The basic reaction that is needed to make soap, called ‘saponification’, cannot occur without some form of lye reacting with some form of oil. Lye is actually a general term for a very strong alkali. There are two alkali’s that can be used to make soap: sodium hydroxide (caustic soda) and potassium hydroxide. Both are considered lye, but the potassium hydroxide is not strong enough to make a solid soap. It is only used for making liquid soaps.