- In the bowl of a food processor, combine the flour, salt, and sugar. Add the butter and shortening and pulse for a few seconds until the mixture has a grainy texture. Add the water and pulse until a ball starts to form. Remove the dough. Form a ball with your hands. Dust it with flour and cover with plastic wrap. Let stand for about 30 minutes in the refrigerator.
- With the rack in the lowest position, preheat the oven to 190 °C (375 °F).
- Roll out the dough and line a 23-cm (9-inch) pie plate, preferably with a removable bottom. Refrigerate for 30 minutes. Prick with a fork and line with aluminum foil. Top with dry beans and bake for 25 minutes.
- Finely grate the zest of one lemon and one lime. Set aside. Squeeze the juice from all the citrus fruit. Set aside.
- In a bowl, beat the sugar, flour, and eggs until smooth. Whisk in the butter, citrus peel, and juice.
- Pour over the crust and bake for about 30 minutes. If desired, brown the top of the pie in the oven under the broiler.
- Remove the pie from the oven, let cool and refrigerate. Chill thoroughly before serving.