Cut lard and butter into ½-inch pieces and freeze until firm, 20 to 30 minutes.

Line rimmed baking sheet with parchment paper. Process flour, sugar, baking powder, baking soda, and salt in food processor until combined, about 3 seconds. Scatter frozen lard and butter over top and pulse until mixture resembles coarse crumbs with visible pea-size pieces, about 14 pulses.

Transfer flour mixture to large bowl. Stir in buttermilk until very shaggy dough forms and some bits of dry flour remain. (Do not overmix.) Turn out dough onto lightly floured counter and knead briefly until dough comes together, 4 to 6 turns. Using your floured hands and bench scraper, shape dough into 8-inch square, about 1½ inches thick. (Dough may be sticky; reflour your hands as needed.)

Using sharp, floured chef's knife, trim ¼ inch of dough from each side of square and discard. Cut remaining dough into 9 squares (2 cuts by 2 cuts), flouring knife after each cut. Arrange biscuits at least 1 inch apart on prepared sheet. Cover sheet with plastic wrap and refrigerate for at least 30 minutes or up to 24 hours. Adjust oven rack to upper-middle position and heat oven to 450 degrees.

Bake until biscuits begin to rise, about 5 minutes. Rotate sheet and reduce oven temperature to 400 degrees. Bake until biscuits are golden brown, 12 to 14 minutes. Transfer sheet to wire rack and let biscuits cool for at least 5 minutes. Serve warm.