If you are serious about your keep, I'd recommend getting your hands on the Stronghold Builder's Guidebook. Its 3.0, but that really doesn't matter. It has everything you need, including ways to make a stronghold scry resistant at a reasonable cost, and the example Cheap Keep is intended to be used as the castle from the Deck of Many Things.
Recommendation: Illusory Landscape (14k, CL7, Craft Wondrous Item) Puts Hallucinatory terrain over 47 stronghold spaces (Cheap Keep is 28)
There sadly isn't any information on lead lining, but 3 inch Iron walls would cost 168000 for the cheap keep (6k/space), and 3 foot earthen, 7000 (250/space), so your DM can wing it from there. I'd probably consider lead half value of iron, then divide again by 6 or 12 for a thin lining to get a cost of 14000 or 7000 for the project.