Lye is typically not artificial if it’s made from sea shells and wood ash like it has been traditionally. Even the industrial chlor-alkali process just uses salt (NaCl) and water so it’s not artificial.
Likewise if you use steel balls to tumble-crush shells into calcium carbonate powder (don't know if they do, or if it's even a product, but neither are the point here).
"We are required to inform this table that your naturally wild-caught salmon had, briefly, at one time, a small hook inserted into its mouth. It was otherwise wholly without artificial feed nor other additives."
How do you write a law that slices between those ideas and hexane, clearly?
You can probably begin by broadly calling petroleum and petroleum products artificial.
Where does salt fall here?
Why isn't petroleum natural, when it is plant-based?
What makes petroleum artificial compared to any other substance found on (or in) earth?
It seems you are proposing that "any food that has had a petroleum product added to it at any stage is artificial", which is an oddly narrow focus.
For that matter, does this definition of "artificial" extend to the range of substances that can be synthesized with bio-feedstock?
To expand on our discussion, would this mean that ethanol made other feedstock is natural, but made from petroleum is artificial?
There's approximately 0% chance that the typical pretzel you bought is made with dye derived from wood ash.
By that standard is anything artificial? Oil comes out of the ground, after all. At least with "natural" colors you can argue the actual molecule was synthesized by a plant and we're just purifying it, whereas for industrially produced lye it's entirely man made.