For the crust, combine the flour, butter, shortening (or lard), salt, and sugar in a food processor. Pulse until the flour looks a little damp (rather than powdery), with tiny bits of fat still visible. Alternatively, combine the ingredients in a large bowl and quickly work the fats into the flour with a pastry blender.
Add 1 to 2 tablespoons ice water. Continue to pulse the dough until it comes together in rough, stiff clumps; if there is unincorporated flour in the bottom of the bowl, sprinkle in a little more ice water.Transfer the dough into a bowl and gather together into a flat disk. Wrap in plastic and chill at least 1 hour.
On a lightly floured surface, roll the dough into a 12-inch circle. Transfer to a 9-inch pie pan. Crimp the edge, trim off excess dough, and chill for 1 hour.
Preheat the oven to 400 F. Lightly oil a 15-inch piece of foil and lay it, oiled-side down, onto the crust; press down to line the crust snugly. Fill with beans or pie weights. Bake until the edges begin to brown, 10 to 15 minutes.
Reduce the oven temperature to 350 degrees F. Carefully remove the beans (or weights) and foil; return the crust to the oven and bake until it no longer looks moist, 8 to 10 minutes. If it bubbles at this point, gently press it down with the back of a spoon. Brush the beaten egg yolk over the crust, then let cool completely, 1 hour.
For the filling, whisk together the lime zest, eggs, all-purpose flour, and sugar in a large bowl. Stir in the cream, lime juice, orange juice, and orange liqueur.
Pour the filling into the cooled, parbaked pie crust. Place the pie in the lower third of the 350 F oven and bake until nearly set in the center (a knife inserted halfway between the edge and the center should come out clean), 40 to 45 minutes.
Remove pie from oven and cool on a wire rack; serve still warm if you can, dusted with powdered sugar and garnished with whipped cream and fresh lime zest.