I use lye water in the washing machine instead of bought detergents, it works best with a pre soak. Sometimes I manage to include some soapwort towards the end of the lye cooking, it really makes a difference with fabrics, but I don't bother if I'm going to use it for the dishes or cleaning other surfaces.... Lye is really effective on raw wood.
Unfortunately I can't say what it's effect on plants/soil is like, as my washing machines in the basement in a very mediaeval hilltop village, plummed in to the sewage system, and any changes would certainly be noticed, like perforating walls a metre thick.... but most of my neighbours aren't plummed in at all.... bathrooms appeared here in the 60s, often as a closed in balcony stuck on the back of the house, with a tube sending black/grey water down the rockface. But I have a LOT of bamboo spreading below the drains.
Tried an experiment with lye, mixing it with vinegar to neutralizer the pH then using it as a fertiliser for some Musa /Japanese banana plants... they love the potassium.
I make lye with one part sifted HARDWOOD Ash and 5 parts water, in an old copper pan, mixing on a simmer for a couple of hours. This way I get to make my own copper sulphate (?), which forms on the rim, should I ever need it....
Here near Rome Lye water is/was known as Bucato, which literally means laundry (in Italian its officially called Lisciva). I also use it to cure green olives, or you can throw 'em directly into a pot or bucket of ashes...