I don't think this is right. Once the oils are completely saponified, meaning that the chemical reaction with the lye is complete, there is no more lye. The chemical reaction turns the lye and the oil into soap (and it emits a LOT of heat in the process). For cold process soap (which is what my wife and I make), the reaction takes approximately 12 hours. After that, the soap is safe to touch...because there isn't any more lye. It's not like after the soap is made, there is still lye in it. If there was, using soap would cause chemical burns. During the 12 hours, however, the mixture can burn because there is still lye that hasn't yet combined with some of the oils and been turned into soap.
I meant within the first few hours after making it. For cold process soap, it takes a couple of weeks to cure. For hot process soap, it can only take a few hours.