Prepare the apple cider by freezing for a few hours until it reaches a slushy consistency.
Add the lye to the partially cider and stir until completely blended. It will melt, heat up, and may change color. Set aside in a safe place.
Measure the oils and butter and melt over low heat until completely melted and heated to 140 degrees. Set aside to cool. Prepare your soap mold and any color or fragrance you are using.
When the oils and cider have cooled to about 110 degrees, pour the cider into the melted oils and blend using a stick blender. Mix until "trace" is achieved, or the soap thickens slightly and a trail of soap rests on top of the batter rather than immediately sinking in. Add desired fragrance or color, stirring in by hand.
Pour into a soap mold, gently smoothing out the top. Place at room temperature to cure. Un-mold after 24 hours, cut into bars, and allow to cure for 2 weeks before using.