I have been playing with some soap recipes, which sound similar to the ingredients you have mentioned. Bought a book with recipes, calling for olive oil and I think they all have lye in them.
I did that because the glycerine I was using, got too expensive. Well, I only attempted a very basic one, but the first attempt I did didn't seem to turn out so good.
I brought both the oil and the lye/water solution each up to 130 F before mixing the lye into the olive oil and stirred every few minutes until I thought it was time to pour into some greased molds, but in less than a day there was a layer of oil on the surface of the soap. I waited a while and decided to pour it all back in a pot and heat it up again and stir some more, until it looked more like thin mayo and repoured into the molds.
Well, they look better, but still not like anything I can pop out of the molds.