Actually a solution made with 4 kg of commercial NaOH in 4 L (4 kg) water will have a specific gravity of 1.54. You do
not have to measure specific gravity to make a consistent lye solution if you are using commercial NaOH of known purity. You can use specific gravity OR you can use a decent scale. Either way, you can get an accurate, repeatable result.
Even if you
do choose to measure specific gravity as a check on the concentration, it does
not have to be in the 1.250-1.275 range for making soap. I use NaOH solutions with specific gravities ranging from 1.28 to 1.54 and get good results from them all.
It is
your choice to use lye solution in the 1.25 to 1.28 range, because you have learned this method makes good soap for you. I can see why you have no reason to change, and that is fine, but you may want to broaden your understanding of soap making.
Just because your method works for you, doesn't mean other people are wrong if they use another method. Your method is valid. And so is his. And so is mine.
Study the chemistry and math of saponification in more depth and learn other ways of thinking about how to make soap. You might still prefer your method, and again that is fine, but with more knowledge, you will understand your way is not the
only way.
As long as I have paper and pencil, I can calculate a soap recipe. Online
soap recipe calculators have only been around for 20 years or so, but soap makers did just fine before that time without the internet, hand held calculators, or hydrometers.
Your assumption that I can't make soap without a calculator is no more valid than if I would assume you can't make soap if your hydrometer breaks. If you understand the chemistry and math of saponification, you have the tools that will let you use other alternatives if you can't use your usual method.