Lime is a rock, right? Rocks are found in mines. Many people have complained that lime is a finite resource in the world, and although this would not technically change that, it basically would, and more importantly it seems fairly realistic to me. My suggestion is that either
1. Lime is treated like a type of ore, that is, some tiles give lime boulders instead of rubble or metal. Then players who need lime badly could deliberately seek out lime deposits in their mines.
or
2. Lime is found randomly when sifting rubble. Then lime can't be farmed as easily, but it adds a steady income of it and people can buy and sell it on the market as needed.
I'm not sure which of these is more realistic as far as how lime behaves in real life, but one of them is probably more realistic than just having lime not exist underground, and it solves a problem for older towns that have used up all the lime nearby on the surface.