In a large mixing bowl, dissolve yeast in water. In a 1 ½ to 2 quart pan, combine milk, lard, salt, and sugar; heat to 110 degrees and add to dissolved yeast. With a dough hook or a spoon, beat in 3 cups all-purpose flour and the whole-wheat flour until dough is stretchy. Add about ½ cup all purpose flour to form a stiff dough. (Mixing by hand) - scrape dough out on a floured board and knead, adding as little flour as possible to prevent sticking, until dough is smooth. Place hand mixed dough in a greased bowl; turn over to grease top. Cover dough with plastic wrap and let stand 1 hour at room temperature. Punch down dough and knead on a lightly floured board to expel air. Roll ¼ of the dough out at a time into a rectangle about 1/8 inch think. Cut 6 equal pieces. Place on light floured pans and lightly cover with plastic wrap. If you work quickly, you can let cut sopapillas stay at room temperature up to 5 minutes; otherwise refrigerate them until all are ready to fry. In a deep 3 to 4 quart pan, heat 1 ½ to 2 inches salad oil to 350 degrees on a deep-fat frying thermometer. Fry 2 or 3 at a time. When they begin to puff, gently push the portion where the bubble is developing into hot oil several times to help it puff evenly. Turn several times and cook until pale gold on both sides, 1 to 2 minutes total. Drain on paper towels.
Serve immediately or keep warm until all are fried. Or if made ahead, cool, cover and chill up to 2 days, freeze to store longer. To reheat, bake, uncovered, on baking sheets in a 300 degree oven, turning once, just until warm, 5 to 8 minutes. Do not overheat (will become hard) Makes 2 dozen. Serve drizzled with honey or syrup, or sprinkled with cinnamon-sugar or powdered sugar.