Simply Carrot

Combine chilled carrot juice with distilled water, carefully stir the lye into diluted carrot juice. Set aside until 100-110 degrees. Melt the coconut oil, then add to the other oils. Combine the warm oils with the cooled lye solution. Using a combination of hand stirring and an immersion blender, stir the soap until it reaches light trace.
At trace, 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, move it to a cooler location. Keep soap in mold for 1-2 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. Cure for 5-6 weeks.