Measure out butter, water and shortening and place in refrigerator to chill.
Sift together, flour, salt and sugar, in large bowl.
Mix in shortening with your fingers and coat it with the flour. Add the cold butter cubes and mix it into the flour with a pastry blender. Work quickly so butter doesn't melt. This is the key to a good crust.
Once the mix looks like coarse cornmeal you can start adding drops of ice water a little at a time and mix it in.
Use enough water until you can form a ball of dough and then split it in two and wrap each disk and place in plastic wrap and refrigerate for at least 30 minutes.
Filling
Once your apples are cut and placed in a large bowl, add lemon juice to coat Apples. Mix, flour, brown sugar, cinnamon, and nutmeg in a smaller bowl and sprinkle over apples to coat generously.
Preheat oven to 450 degrees
Take out one disk of dough and roll out to 2" larger than your pie plate. Place into the pan and fill with apples. Adding any remaining sugar mix on top of apples.
Take out second wrapped disk and roll out to 2" larger than pan. Take pastry cutter and slice even slices and weave on the top.
Make an egg wash and brush on top of crust, moderately.
Place in middle rack of oven on a cookie sheet. Bake for 40 - 50 minutes, checking on it the last few minutes.
Notes
If you don't feel up to the challenge of a lattice crust, you can just lay it on whole. Just make sure to cut a few slits to let steam escape.