Cut flour, lard, 1/4 cup cold butter, and 1 1/2 teaspoons salt together in a bowl with a pastry blender until mixture is the consistency of coarse crumbs. Make a well in the center; pour in ice water. Mix with a fork until begins to come together; use hands to form into a dough ball.

Turn dough out onto a lightly floured work surface; knead until smooth and forms a firm ball, about 2 minutes. Wrap dough tightly in plastic wrap; refrigerate until chilled, at least 2 hours.

Preheat the oven to 350 degrees F (175 degrees C). Line a baking sheet with a silicone baking mat.

Combine steak, potatoes, onion, turnip, 1 1/2 teaspoons salt, black pepper, and cayenne pepper in a bowl.

Beat egg and 1 teaspoon water together in a small bowl.

Divide dough into 4 equal rounds; roll each out to about 1/8-inch thickness and 8-inches in diameter. Brush each dough round with egg wash.

Place 1/4 steak mixture slightly off-center on each dough round; top each with 2 slices butter. Fold dough over filling to form a half moon shape; press edges together to seal. Trim excess dough from edges. Transfer pasties to the prepared baking sheet; crimp edges with the tines of a fork. Poke top center of each pasty once with fork; brush tops with egg wash.

Bake in the preheated oven until browned and bubbly, about 1 hour. Cool on a wire rack for 5 to 10 minutes.