Combine the flour, sugar, and salt. There are many ways to cut the butter and shortening into the flour, but I prefer to use a combination of my food processor and my hands. The food processor breaks up the fat quickly, so there is less time for it to get warm. Put the butter in the machine in 3 parts and pulse 2-3 times. By the time you've added all of the butter, some of it will be completely blended into the flour and some will be in large pea-sized pieces. Add the frozen shortening and pulse until it too is pea-sized pieces (it is much softer, so it breaks down quickly). Add the ice water to the dough 3 tablespoons at a time and pulse just once to combine. If you pulse too much at this point you will continue to break down the butter too much.
Once you've added all of the water pour the dough out onto the counter, or into a large flat bowl (pasta serving bowl works well). It may still need some water, so I like to do the rest by hand so that I don't break down the butter too much.
First, try pressing the dough together to determine if it is too dry. If it isn't holding together, or there is still powdery flour then sprinkle a couple more tablespoons of water evenly over the dry spots and try pressing together again. Fold the dough several times over itself with a bench scraper. The dough should come together without falling apart, but not be too mushy with water.
Press into a log and cut into 2 pieces. Form the dough into two disks and wrap it with plastic. Chill for at least 1 hour, but this can be done the day before, or put it in the freezer for a couple of weeks (Allow to defrost overnight in the refrigerator, not the counter or it will be too soft).
Once the dough is chilled sprinkle flour onto your counter, a silicone mat. Roll the dough out from the center, adding a little flour and turning the dough a 1/4 turn to make sure it isn't sticking too much to the surface. If you use a silicone mat you will use less flour.
Make sure the dough will fit the pan you are using. There should be about 2 extra inches around the pie plate. Use your rolling pin to transfer the dough to the pie plate. Put the rolling pin in the middle of the dough and fold the dough over the pin to lift it.
Place the dough in the pie plate, don't force or stretch it or it will shrink away from the sides as it bakes. Put the pie plate with dough into the refrigerator to rest while you make the lattice.
Roll the next disk of dough out just as you did the first one, but this time you need to build it on a sheet of vinyl or a silicone mat so it can be lifted. Now you will use a pastry wheel to cut strips in the dough. Depending on your personality you can measure the strips or eyeball them. When you are finished cutting the strips remove every other one and set aside.
Fold up every other one of the remaining strips to the middle point. Lay one of the pieces that you had set aside over the strips that are laying flat. Unfold the strips and repeat with the next set. Continue until you get to the end of this side and then start this on the other side.
Once the lattice is prepared slide the vinyl or silicone mat onto a cutting board or baking sheet so that you can easily transfer to the refrigerator. You need to let this chill so that it is easier to slide onto the filled pie.
Once the lattice is chilled it will slide easily onto the pie shell filled with fruit. Then you will need to trim the excess length off of the lattice strips. They should fit just over the filling. Fold up the sides of the pie shell and then crimp them in whatever design you choose.
Brush the surface of the lattice, but not the edge of the pie shell, with egg wash. Sprinkle with sugar, I then stick the pie into the freezer for about 15 minutes while the oven is preheating to 425 F. Freezing the dough will help to set the dough so that it won't blow out your design when it goes in the oven.
After 30 minutes, turn the temperature down to 375°F and bake until the fruit is bubbling and juices are translucent. The length of time to bake your pie will be determined by the filling. My peach-raspberry pie took about an hour. You may need to tent the crust if it is browning too quickly as the filling bakes fully.