It’s kind of amazing that you can get a ceramic container where the lid fits snuggly. Some of that comes from modifying the greenware (dried but unfired clay) but I think most of it is exacting tolerances for inputs and processing. Clay from this one quarry. This much water. These building temperatures and humidity. This exact furnace temperature and time.
One can fire a pot with the lid on it in the kiln. They tend to deform together. Of course, this requires that the mating surfaces not fuse together and may also produce a non-rotationally-symmetric interface.
I feel like I've watched videos where people make Japanese and/or Korean ceramic cook pots and I can't for the life of me remember how they kept them from warping, just that they do.
The only trick I do remember is don't glaze the contact point between the two pieces. That not only adds thickness variability, but if glaze touches the bottom of the kiln you fuse to the bricks, so you have to elevate anything glazed, and elevating increases warping.
