This is actually one of my favorite questions. I include sodium hydroxide in my ingredient list for all cold-processed soap, but this is another topic that is up for debate.
You cannot have true soap without lye. Soap doesn't exist until lye is involved. Lye is the ingredient whose chemical process turns oils into soap. It's that simple. If you are buying a handmade cold-processed soap that does NOT include lye as an ingredient, its because they are taking a position that the lye is gone once the oils become soap.
Because the chemical process removes the lye and changes the oils into soap, some soap makers decide to remove it from their ingredient list because it alarms people. As an alternative, you may see "saponified oils of..." listed instead. Those terms mean the same thing.
The requirement isn't there, but I include it anyway as it is an ingredient and a necessary one. I'd rather be transparent and educate customers if they are confused. Want to learn more about cold-processed soap making basics? I have a YouTube tutorial that discusses this and shows you how to make a basic 3 color cold-processed soap. You can catch that video here: https://youtu.be/E7JlAtmsIcM