Most websites say that the lye solution is the correct strength when a small potato or raw egg floats while showing an amount above the surface tension of the water about the size of a quarter. Most sources are unclear about the proper pH of lye water, but it is expected to be somewhere between 13 and 14 (the most alkalotic substances known to man) to be strong enough to saponify oils.
It is difficult to guesstimate an approximate recipe to use the lye water. One person states, "If your lye water will float an egg with only a quarter size showing, boil down 1 gallon of lye water to 3/8 cup. Use 2 cup fats with 3/4 c. concentrated lye water…proceed slowly adding small amounts lye to fats whipping briskly each time."
Another recipe concerning the proportion to ash water to fats can be found here. The author states, "Thirty-five liters of ashes is about the right amount for 2 kilograms of fat (a bushel of ashes for 4 pounds of fat). This proportion is cited in soap-making recipes of the colonial period in the United States, but many of the recipes of that era differ on the proportion of ashes to fat. Put 115 ml (1/2 cup) of lye in the kettle for every 230 ml (1 cup) of fats or oils."
Another soap making website says the ratio of home-made lye water to fats should be "115 ml (1/2 cup) of lye in the kettle for every 230 ml (1 cup) of fats or oils." It goes on to say the mixture should be boiled until it becomes thick, foamy, and rubbery.
This site has a surprisingly well-written article about how to neutralize an alkalotic pH in liquid soaps. In short, boric acid or borax is added to the soap solution, then allowed to precipitate, leaving the remaining soap more neutral and clear. Of course, proper pH testing is necessary to prevent skin reaction (we can handle more acid than alkali). Adding more fat will also bind the alkali in the lye.