It is impossible to make soap without lye. In fact, lye is the essential ingredient in soap making! Lye causes the chemical reaction known as saponification, the reaction that turns fat and water into soap. Without lye, we would all just be rubbing oil on our bodies (not a bad idea, but not soap).
Rest assured, however. There is no lye in the finished product. I carefully calculate all of my recipes using a minimum of 5% superfatting, which means that all of the lye is used up in the process of saponification and some oils are left unsaponified. This leaves a more moisturizing bar with zero lye in the final product.