Mix the flour, sugar, and salt in a large bowl. Add the lard and the butter, and cut them in with a pastry blender until the larger pieces are the size of peas and the mixture begins to clump on the pastry blender. Shuffle through the mixture with your hands, pinching chunks of lard to flatten them.
Add 4 tablespoons of the ice water and mix with a fork. Pinch a clump of dough in your hands: If it feels moist and clumps together easily, it's probably hydrated enough. If it feels really crumbly, add another tablespoon or two of ice water until you can form a baseball-size clump of dough, packing it on as if you were making a snowball. You want to mix the dough as little as possible to ensure it stays tender.
Divide the dough in half and form each half into a flat disk. Wrap both disks in plastic wrap and refrigerate for at least 1 hour and up to 2 days.
Thirty minutes before you're ready to roll out the dough, remove it from the refrigerator and let it sit at room temperature to soften.
Adapted from "The New Midwestern Table" by Amy Thielen (c) Clarkson Potter, 2013. Provided courtesy of Amy Thielen. All rights reserved.