I had no idea Lava would still lather in salt water. That is a bit of information I will store away for future use. Hank, you are a fount of useful information!
I started buying homemade soap at my farmers market and it lathers in hard water, I don't know about salt water, but I even wash my hair with it, no conditioner needed afterwards, either. It cleans my hands much better than commercial soap.
We used to take ivory soap flakes and a little water and add all sorts of stuff to it and make our own soap !!