In a large bowl, prepare the apples and toss them with the lemon juice.
Prepare pie pastry: Cut shortening into flour and salt until pieces are the size of small peas. Sprinkle water, a tablespoon at a time, over a small part of the mixture; gently mix with fork; push to one side of bowl. Repeat until all is moistened. Form loosley into a ball and let stand 5 minutes. Divide dough in half to form into two balls. Flatten one ball slightly and roll into 11-inch circle. Fit it into a deep-dish 10-inch pie plate, letting the edge hang over 1-inch.
Sift brown sugar and white sugar together with the flour, salt, cinnamon and pumpkin pie spice. Then, toss this mixture with the apples.
Spoon the apples into the pie crust in the pie plate, mounding the apples high in the center.
Roll out the remaining ball of pie pastry dough to make the top crust. Place it on top of the pie and flute the edges. Cut decorative slits or openings in the top crust.
Bake 20 minutes, then lower the temperature to 375-degrees and bake an additional 30 minutes. (Cover pie crust edges with aluminum foil for the last several minutes of baking if the crust is getting too dark.)
Cool the pie on a rack for at least 1 hour before serving.