Choose ONLY one set of ingredients -- either the recipe with lard or the recipe with vegetable shortening.
Prepare molds.
Measure shortening, being sure to allow for the weight of the container. Warm in slow-cooker until melted. (This can take a while.)
When shortening is melted, measure water in pitcher and measure lye in a separate container. Take outside, if possible, and mix lye into water (not the other way around!) with wooden spoon. Stir until lye is completely dissolved.
Take lye water back inside and mix into melted shortening. Continue stirring until mixture reaches trace. "Trace" is when you can lift the spoon and drizzle some of the soap into the mixture and it remains momentarily on the surface, leaving a "trace". (The reason for stirring during this time is to keep undeveloped lye from being left in your finished soap.) Now you can stop stirring. Leave the cooker on, though.
After a little while, the edges of the soap will start to bubble up and sort of fold over onto the middle of the soap. The bubbly part will gradually extend toward the middle of the pan. When all of the soap is bubbly -- it will look like applesauce or gloppy Vaseline -- it's finished.
You can now plop it into your mold(s). You might want to tap them on the counter several times to help eliminate air bubbles.
Leave overnight, then unmold and cut. This soap can be used immediately or you can leave it for several weeks to dry out and harden.