Woah, intense! Life has blessed you with a completely fresh start, eh?
About the lye, there could be a misunderstanding since most store owners probably won't have studied chemistry. I can imagine that they see one drain cleaner as being very much like another. They might view something as being "caustica" without it being alkaline - I get the feeling you were probably sold sodium bisulfate, which is used as an
acidic drain cleaner and descaling agent.
If you can make a small lime kiln, or obtain pre-burnt lime, you have access to alkaline materials. It can be as simple as roasting snail shells or seashells to a white heat. Once you have lime, if you can get hold of baking soda you have your route to lye should you need it.
Gently roasting baking soda produces sodium carbonate -
soda ash. Of course, you might well be able to purchase soda ash or washing soda to speed things up a little. Or, as the link suggests, you could obtain it by burning sodium-rich (shoreline) plants. Mixing slaked lime and washing soda produces chalk and lye.
Let's imagine you can't even get hold of either of these forms of soda (not soda water or soft drinks!) - what would you have to do then? Well, assuming you don't want to use lime as the base for whatever reason, and ignoring the fact that sodium carbonate can sometimes be found in the desert in the form of
trona, if you can collect seawater, lime and your own urine you'll be well on the way. By collecting sodium chloride from the sea salt and using the lime and urine to produce ammonia, the determined home chemist can perform the
Solvay process. By following Hou Debang's variation, you could even dispense with the need for lime if you can generate ammonia some other way (I don't know if you've ever experienced opening a bucket of wet cloth nappies, but there's an idea. Breeding babies solely for the purpose of ammonia production is probably unethical, however - not to mention time-consuming and resource-hungry. Baby urine does make nicer ammonia than most adult urine though.)
If you have a solar power set up it would probably be more economical to electrolyse salt solution though, except for the generation of chlorine gas that you'd have to deal with (not to mention the off-gassing of extremely flammable hydrogen). You'd need a semi-permeable membrane for the electrolysis cell to work properly. There's plenty of information available regarding brine electrolysis.
Hope this helps!
