Short lesson on soap:
All "real" soap (i.e. natural soap) is made with lye - either sodium hydroxide for hard soap, or potassium hydroxide for soft or liquid soap.
Lye is a naturally occurring substance. Potassium hydroxide can be obtained by soaking wood ashes in rain water and filtering the liquid to mix with melted fats/oils. This is what people used in the past until sodium hydroxide became widely available.
Lye is mixed with oils and fats and causes the fats to saponify, or turn into soap. The only time you will have trouble with lye in the soap is if the recipe is lye heavy - i.e. has more lye than oils/fats - or if it is cold processed and not totally cured.
Lye burn problems can be avoided by careful handling of the lye mixture, super fatting the soap and hot processing it, or allowing plenty of time for curing cold processed soap. Super fatting means that there is more oil or fat in the soap than the lye can saponify, so the soap is moisturizing, gentle and humectent (moisture attracting).
The only way I have found to avoid using lye in making soap is to buy a base soap from someone else and let them handle the lye. I prefer to control my own soap ingredients, so I make my own. With lye.
Hand made soap is a natural soap. They are more gentle than the "beauty bars" or commercial soaps on the market because hand made soaps have the glycerin still in them and the best are super fatted. Commercial soaps have the glycerine removed or are detergents, not natural or true soaps.
Natural soap does not leave your skin feeling tight and dry like commercial soap, nor does it have those annoying grey things that rub off your skin. (although, you may have them for the first few washes with natural soap. They are the junk that detergent/beauty bar soap leaves behind - dead skin mixed with sludge. eeww)
What makes a soap organic or vegan or just natural is the oils, fats and additives used in creating the soap. Some ingredients (such as scents or colors) are only available as non-organic or non-vegan items. As stated before, all handmade soap is natural.
The so-called glycerin soaps are either detergents or clear soaps. True clear soap is varying shades of amber, depending on the formula. All natural soap has glycerin in it.
Side note: NEVER use Red Devil brand lye in your soap making. They have been adding aluminum shavings and other ingredients to their lye. These are undesirable in soap making. Only use 100% sodium hydroxide or 100% potassium hydroxide to make your soaps.
End of Lesson.
Edited for spelling and to add: Why are you not wanting lye in your soap?PM me and I will send you a sample of my oats & honey goat milk soap to try. (Just need postage.)