You can use some of your lye to make lime by mixing it with calcium chloride, if you prefer using a limetek.
Another route - the old skool way - is burning limestone. An oxy-propane torch provides fun, but make sure you wear welding glasses - it gets very bright! Hydrating calcium oxide its also highly entertaining (for a simple-minded nerd like me, at least). Again, eye protection is a must.
As far as extracting goes, I'd say you're best off just getting to grips with the fundamental principles of it so you'll have the flexibility to adapt your methods to the resources available.