(National City, CA, USA)
Do you need FDA permission to sell soap with lye?
The answer to that can be found on the USA Food and Drug Administrations website. Their page titled Is It a Cosmetic, a Drug, or Both? (Or Is It Soap?)
can answer this question for you.
Basically it says that if your product (made of alkali salts of fatty acids...ie. lye and oils) is just soap with the sole purpose to clean, then you do not need approval.
If it is also intended to beautify or moisturize, then it is a cosmetic.
If your soap is intended to cure treat or prevent a disease or condition then it is a drug.
Read the article...especially the last three paragraphs starting with the part titled "And what if it's 'soap'?".