Materials like lace rock and other limestones have other things besides carbonates, but carbonates are the main buffer.
When the water is acidic more of the rock dissolves. This releases more carbonate and minerals, and the GH, KH and pH rise. (Usually- I see your test when the pH went down)
When the water is more alkaline less of the rock dissolves. Whatever is removing the carbonates from the water can get busy doing that, and the pH comes down.
Each type of limestone (including lace rock) tends to stabilize the pH at a different value. Almost always in the mid 7s to mid 8s. It is the combination of whatever minerals are in the rock, and how they interact in the water. When they are all doing whatever they do, but in some sort of balance, that is what is called equilibrium. The reactions are still going on, but one is balancing the other, and the tank chemistry is stable.
The relationship between carbonates and pH is not cast in stone. The pH can vary, even going down when the carbonates are rising. There is simply something else in the water that is also altering the pH, and the equilibrium is somewhere between the two materials.
Anyway, interesting to see the test results.
What are the values of the tap water? (Does not matter if it has Prime or not, but don't bother to add it) GH, KH, pH.
If you test the tap water after it has sat out overnight, perhaps 24-48 hours, does the pH change?
How about trying this:
Rinse the 'desert sand' really well, then see if it still has the same effect.
Do you have that lace rock in any other tank?