Quicklime vs hydrated lime for making lye water

For my entry to Atlantia’s Royal Scientist at KASF 2025, I conducted an experiment investigating if hydrated lime could be used for making lye water rather than the quicklime that medieval recipes called for. Medieval recipes call for adding water to ash and quicklime to produce lye water. But adding water to quicklime produces hydrated lime, so it seems like ash, hydrated lime, and water would give the same results. The results were inconclusive. I was not able to determine with what I had available as to whether I had produced potassium hydroxide or if I had potassium carbonate. I will conduct some other experiments and come back to this.