In bowl combine flour, baking powder, salt, and sugar. Add in lard or shortening and combine.
Add warm water and milk to a bowl. Combine into a dough and knead by hand or using mixer or food processor. Cover with plastic wrap and let sit for 30 minutes.
Heat oven to 200 degrees. Heat oil in heavy duty skillet to 350 degrees (at least 2 inches deep).
Working in batches roll out a portion of dough until about 1/8 inch thick. Cut into 4-inch by 4-inch thick square. Cover with plastic wrap
Fry individual squares until golden brown on both sides. Spoon hot oil over top to help rise. Total frying time should be about 2 minutes.
Place cooked sopapillas on a plate covered with a paper towel. Keep warm in a 200-degree oven until ready to serve.