In a food processor, combine the flour, sugar and salt. Add the butter and shortening and pulse until tit forms pea-sized pieces. Add the water and pulse just until the dough starts coming together. Remove the dough from the food processor. Using your hands, form the dough into a disc. Cover in plastic wrap and refrigerate for 30 minutes.
On a lightly floured work surface, roll out the dough and line a 9-inch (23 cm) pie plate, preferably with a removable bottom. Refrigerate for 30 minutes.
With the rack in the lowest position, preheat the oven to 375°F (190°C).
Prick the pie crust with a fork and line with aluminum foil. Top with dry beans (or ceramic baking beans) and bake for 25 minutes. Remove the beans and foil.
Filling
Meanwhile, finely grate the zest of one lemon and one lime into a bowl. Squeeze the juice from all of the citrus fruit into the bowl. Set aside.
In another bowl, beat the sugar, flour, and eggs until smooth. Whisk in the butter, citrus zest and juice. Pour into the crust.
Bake for 30 minutes. Brown the top of the pie in the oven under the broiler, if desired. Remove from the oven and let cool on a wire rack. Refrigerate for 4 hours or until chilled.
