My dictioniary defines lye as 1. A iiquid obtained by leaching wood ashes; 2. KOH, or 3. NaOH .
#1 is lacking in useful information in re straightforward inorganic chemistry.
Sea water must be a virtual chemical hodge-podge, and not globally uniform considering all the stuff that is carried into the seas/oceans by rivers laced with all manner of solutes of lithological origins.
But, without checking at the moment, I believe the can of lye on my cupboard (or workshop) shelf consists virtually exclusively of KOH.
My comment was based on looking at several sites when I googled “how to make lutefish.” Lye leached from birch ash was considered the best for taste. The process consists of a lot of soaking, drying, rehydrating, etc. and you should Google if you want to know more. Sea salt as it has been used for hundreds and even thousands of years works fine. It is 60% sodium cloride, and 40% other minerals. Only in recent times has abnormal content been a problem that needs consideration.