An idea
This is what I use for the mechanic soap I make on occasion. A mixture of orange and eucalyptus essential oil.
The primary bulk of modern "hard cleaners" (oil and stain fighters) use orange essential oil, as it breaks down the bonds of the oil to fabric and skin.
Most industrial level cleaners use Eucalyptus. The main ingredient in Eucalyptus essential oil is Menthol, which is an alcohol that will absorb oils.
The lye soap in and of itself is actually a salt (acid + base = salt... Lye + amino acids in oil = salt) which absorbs oils that are broken free.
What you end up with is the Orange breaks the bond between oil and fabric, the soap (which a soap molecule has one end attracted to oil, the other end attracted to water) pulls the oil away from the fabric and into the water, and the Eucalyptus left on the clothes will prevent "rebonding", where the oil breaks loose of the hold and reattaches to the stain (thus, the stain spreads) and keep the oil where it belongs... off your clothes.
This is the general premise of my mechanics soap, I believe 100% that it will work great for stain removal, but I will admit I have not tested it for this purpose.