|MadSci Network: Chemistry|
As you mentioned, there is a reaction going on in the making of lye soap, and that reaction is basically between a triglyceride and a base (and some water to dissociate the base's ions). Lye is great, as it is a high pH base. Lye is in modern times normally characterized as sodium hydroxide (NaOH) and sold as such. In the days of yore though, any base that was used in soap was called a "lye." The "lye" you get from burnt wood ashes is potassium hydroxide (KOH) which is chemically very similar to sodium hydroxide (NaOH). The role of both types of lye is identical in the formation of soap. Incidentally, in my research of this question, I made some soap myself from some ashes from my fireplace and some bacon fat. The soap wasn't the best quality, but I noticed something interesting along the way: wet ashes on your fingers feel very soapy. This is because your skin cells are reacting with the ash and the water to make a thin layer of soap! Luckily no harm was done, and my new soap did get the rest of the ashes off of my hands.
Some basic soap making and history web sites:
The Soap Factory
The Soap and Detergent Association
Take Care and Be Safe,
Steve E. Williams
Rock Star and Science Demonstrator
Pacific Science Center, Seattle, Washington, USA
Try the links in the MadSci Library for more information on Chemistry.