Wearing protective gloves and eyewear, carefully stir the lye into the distilled water, then set the lye solution aside in a safe place to cool for about 30 to 40 minutes or until the temperature drops to around 100 to 110°F (38 to 43°C).
Melt the coconut oil, then add to the other oils. Add the coconut milk to the warm oils and use an immersion blender for a few seconds until thoroughly combined.
Add the lye solution to the warm oils and coconut milk mixture. Using a combination of hand stirring and an immersion blender, stir the soap until it reaches a light trace. (See photo, right.)
Pour into a prepared mold. Cover lightly with a sheet of wax or freezer paper, then a towel or light blanket. Peek at the soap every so often; if it starts developing a crack, uncover and move it to a cooler location.
Keep the soap in the mold for 1 to 2 days, or until it's easy to remove, then slice it into bars when it's firm enough not to stick to your cutting tool.
To make shampoo sticks, cut each bar into thirds. Cure on coated cooling racks or sheets of wax paper about 4 weeks before using.