I think we might be getting hung up on semantics.
What we as soap-makers refer to as being a 'lye solution' is the mixture of lye and water.
What we refer to as being a 'lye concentration' is the ratio of how much lye to water, which we often speak of in terms of percent. For example, a 1:1 ratio is a 50% lye concentration. The higher the lye:water concentration, the quicker the soap will trace and set up/harden, but that has nothing to do with the lye to fat ratio. That's looked at as a separate thing.
The ratio of lye to fat is what we term as being a 'superfat'. Basically, a low superfat (more lye to oils) will make for a more cleansing (harsh) soap, and a high superfat (less lye to oils) will make for a less cleansing (more gentle feeling) soap.
In any given soap recipe, the lye amount is calculated according to the individual SAP# (saponification number) and amount of each oil/fat in the given recipe, i.e., how much lye is needed to turn any given oil/fat into soap. In a perfect world, if you set your superfat level at 0% when making your calculations, in theory you would have the exact amount of lye to 100% completely saponify all your oils with no oils or lye left over.
But the world is not perfect and SAP#'s are not set-in-stone. Since SAP #'s vary depending on where your oils/fats were sourced, it's very possible for one to end up with a lye heavy soap with a 0% superfat, or maybe a slightly superfatted soap at the other end of the spectrum. Because of this fact, online
lye calculators base their SAP#'s for each oil/fat on the average SAP range for whichever individual oil/fat. And since lye-heavy soaps are very unpleasant on the skin, online
lye calculators have also set up their superfat box with a built-in default 5% superfat level (which you can change if you desire), which insures against lye heavy soaps.
IrishLass