Preheat the oven to 400 degrees . In a large bowl, combine the chicken, frozen vegetables, soup, milk, thyme and 1/2 teaspoon pepper; transfer to a 7-by-11-inch casserole dish.
Using a food processor, combine the flour and teaspoon salt. Add half of the lard and pulse until the mixture resembles sand. Add the remaining lard and pulse until only pea-size lumps remain. Add the ice water and pulse briefly until the dough holds together. Turn out onto a floured surface and gather the dough into a ball. Roll out the dough into an 8-by-12-inch rectangle. Drape the dough over the rolling pin to transfer to the casserole; crimp the edges. Cut 3 slits in the dough for vents and brush all over with the egg.
Bake the casserole until golden-brown and bubbling, 40 to 45 minutes. Let sit for 10 minutes before serving.
