Cut flour, lard, cold butter, and 1 1/2 teaspoons salt together in a bowl with a pastry blender until mixture has the consistency of coarse crumbs. Make a well in the center and pour in ice water. Mix with a fork until mixture begins to come together; use hands to form into a dough ball.
Turn dough out onto a lightly-floured work surface and knead until dough is smooth and forms a firm ball, about 2 minutes. Wrap dough tightly in plastic wrap and refrigerate until chilled, at least 2 hours.
Preheat oven to 350 degrees F (175 degrees C). Line a baking sheet with a silicone baking mat.
Stir steak, potatoes, onion, turnip, 1 1/2 teaspoons salt, black pepper, and cayenne pepper together in a bowl until evenly-combined.
Beat egg and 1 teaspoon water together in a small bowl.
Divide dough into 4 equal rounds and roll each round out to about 1/8-inch thickness and 8-inches in diameter. Brush each dough round with egg mixture.
Place 1/4 of the steak mixture slightly off-center on each round of dough, and top steak mixture with 2 slices butter. Fold dough over steak filling to form a half moon shape and press edges together to seal. Trim excess dough from edges of pasties. Transfer pasties to the prepared baking sheet and crimp edges with the tines of a fork; poke fork 1 time into the top center of each pasty and brush tops with egg mixture.
Bake in the preheated oven until browned and bubbly, about 1 hour. Cool on a wire rack for 5 to 10 minutes.
