Mix the 2 1/2 cups flour with the salt, cut in the lard until pea-size pieces remain, and add the ice water 1 tablespoon at a time until the dough holds together.
Divide the dough into 2 disks, wrap, and refrigerate for 30 minutes while heating the oven to 425°F with a sheet pan on the lower rack.
Toss the apples with the sugar, 3 tablespoons flour, cinnamon, nutmeg and lemon juice.
Roll one disk into a 12-inch circle, fit it into a 9-inch pie plate, add the apples, and dot them with the butter.
Roll the second crust, lay it over the apples, trim and crimp the edges, cut 5 vents, and brush with egg wash.
Set the pie on the hot sheet pan, bake for 20 minutes, lower the oven to 375°F, and bake 40 to 45 minutes more until the crust is deep golden and thick juices bubble through the vents.
Cool for at least 3 hours before slicing so the filling sets.