Check out this link from EWG. Really good website for a ton of serious reading.
http://www.ewg.org/skindeep/ingredient/706075/SODIUM_HYDROXIDE/
I wouldn't use the EWG website, personally. It is another "fear mongering" website. If you look at half the stuff listed on EWG website(s), everything causes cancer. They seem to use "sensationalism" to promote their purpose/claims.
PersonalCareTruth.com uses scientific research to back up their claims/opinions/results.
Ah, the "natural" conundrum...
As for the "is lye natural" debate...commercial lye that we purchase is not natural, but as other people have stated, it is a "processing agent" more than an "ingredient" (even though I'm an advocate of listing it on your ingredients label). If you push the "natural" definition...unless you pluck it off a tree or dig it up from the Earth and use it as is, it isn't "natural". Unless youre rendering your own fats or extracting your own vegetable oils, they have been processed through either chemical or mechanical means. Same with EOs. On the other end of "natural", there are "nature identical" FOs and oxides. We use electric stick blenders, silicone molds, etc...so everyone's definition of "natural" may be different, but I'll share mine (and my business "model", so to speak):
Natural IMO: Herbs or Clays as colorants, EOs as scent...I personally use vegetable oils, but animal fats are obviously natural also. All these things are "naturally derived", meaning they are found in nature, though possibly not in the form they are used in. EOs are found in the plant matter and need various extraction methods to obtain them...but they are naturally sourced. Same with herbs and clays.
I obviously use commercially produced lye for safety and consistency. No way around that. (Yes, you can make your own potash, but I wouldn't for products I intend to sell to the public.)
I'm not so sure how I feel about oxides (I don't use them) or "nature identical" ingredients. Micas are mostly lab created to avoid lead contamination found in the natural source, so obviously not "natural", but probably safer than the natural version (I don't use Micas either). I do use a "natural" Almond Fragrance that is derived from Cinnamon Bark (benzaldehyde), so I still consider that natural - not natural Almond, but Cinnamon is natural in my book.
Keep in mind that my opinion of "natural" may be different than others...I don't expect you to substitute my judgment for your own...just sharing