"...recommended lye solution strength for CP? SoapCalc has a default of 38%...."
To be persnickety about it -- that 38% default is NOT the solution concentration. This is the amount of water figured as a % of the oil weight. When a recipe uses the water as % of oil weight default, the actual lye solution concentration will vary depending on the saponification value of the fats in the recipe. That just doesn't make any sense from a chemistry perspective.
One can calculate the NaOH and water required in terms of solution concentration or as a water:lye ratio, but neither of these options is the default option in SoapCalc.
Most people start with a 27-28% NaOH solution concentration (this is the lye concentration number, not the "water as % of oils" number), but many soapers at least try a 33% or 40% NaOH solution concentration to see how it works for them. Some recipes work better than others.
Lower lye solution concentration => more likely to reach gel, slower to trace, higher possibility of streaking and mottling, better for recipes with high % of solid fats, more predictable for beginners.
Higher solution concentration => less likely to gel, faster trace, better for recipes with high % of liquid fats, trickier with fragrances that are prone to seize or rice.