In a well vented room or outdoors, wearing gloves and safety goggles, carefully and slowly pour the lye into the water. Stir gently.
Once the lye water has turned from cloudy to clear, leave it to cool until the temperature is 100 degrees.
Weigh tallow and coconut oil out and put into a pot to melt. Then add the olive oil and the castor oil. Check the temperature of the oils. You want it to be 100 degrees F. Let cool if necessary.
Carefully pour the lye water into the oil mixture
Use an immersion blender to mix the soap. After a few minutes, it will get creamy, and start to thicken. Mix until it has reached trace, the light pudding consistency.
Add the essential oils and blend again to incorporate.
Pour soap into molds, top with cardboard or wax paper, and wrap molds in towels.
After 24 hours, remove soap from the mold. Let cure in an area with good airflow for 4 weeks.
Notes
To help keep fumes down place your lye water container in a metal bowl of ice.