NaOH will tend to thicken soap, like Megan said.
I would expect adding NaOH would tend to reduce lather in a KOH soap, not increase it.
The problem with using a blend of NaOH and KOH to make liquid soap is that thickening due to sodium ions only happens over a narrow range of sodium concentration. The exact amount of sodium needed will vary depending on the fatty acids in the soap. Not to say it won't work, because it will for soap that's sufficiently high in the right fatty acids.
But it might be easier and better in the long run to thicken by adding table salt or grated sodium soap to the finished liquid soap. Then you can dial in the dosage to exactly what is needed for that particular soap -- you don't have to guess in advance about how much is needed.
