To make the dough, combine the flour, butter, lard, and salt in a bowl, put the bowl in the freezer, and chill for 30 minutes.
Remove the flour mixture from the freezer and use a pastry cutter to break up the butter and lard into pieces the size of a dime. Make a well in the center, and pour in the ice water and the egg. Mix with your hands until the dough comes together, but don’t worry about getting it too smooth; bits of butter should still be visible in it. Cut the dough in half and flatten each half into a disk. Wrap each one with plastic wrap, and refrigerate them for at least 30 minutes or as long as 3 days.
Adjust the oven rack to the middle position and preheat the oven to 450°F.
To make the filling, combine the berries, sugar, nutmeg, and lemon zest in a bowl. Cover it with plastic wrap and set aside at room temperature for 30 minutes.
Toss the berry mixture with the flour. Add the crème fraîche and mix until the berries are coated.
Roll out the pie dough on a lightly floured surface to form two rounds about 12 inches in diameter. Pick up one round by rolling the dough onto the rolling pin, and lay it in a 9-inch pie pan. Gently press the dough over the bottom of the pan and up the sides, leaving a lip around the edge.
Spoon the berry mixture into the pie shell and dot with the butter. Place the round of dough over the filling. Trim the excess dough just to the border of the pie pan and crimp the edges (or seal the pie by pressing the edges with a fork). Brush the top of the pie with the beaten egg and sprinkle it with the sugar. Cut slits in the top crust to allow steam to escape.
Bake the pie for 15 minutes. Then reduce the oven temperature to 375°F and bake it for another 45 minutes, until the crust is very golden brown and the filling is bubbling in the center. Let the pie cool for at least 1 hour before slicing.