Prepare the pie crust, and set aside.
Add berries, sugar, and lemon juice to a large saucepan.
Cook over medium heat until warm and juicy (about 7-10 minutes), gently stirring occasionally.
Pour (or spoon) about ½ cup of the juice from the saucepan into a glass measuring cup or bowl. Add cornstarch into the juice; stir until smooth.
Note: if using frozen berries, and there is a lot of liquid still left in your pan after pouring off the ½ cup of juice to thicken, then drain another ½-¾ cup of juice off and discard.
Pour the cornstarch mixture back into the pot of berries. Bring it back to a simmer, gently stir (be careful not to mash the berries) until thickened (about 5-10 minutes).
Remove from heat. Allow mixture to cool for about 10 minutes, and then pour into unbaked pie shell.
Add top crust with holes cut for steam to escape (or make a lattice top).
Pinch the edges of the top and bottom pie crusts together, and flute the edges. Add pie crust cutouts, if desired. And then sprinkle lightly with granulated sugar.
Bake at 400° Fahrenheit for 45 minutes. Check the pie after 25 minutes, and if the crust is getting too brown, place a piece of tinfoil over the top of the pie crust.
Remove to a wire rack to cool. Allow the pie to cool several hours. Once cool, cover the pie with saran wrap, and refrigerate it. This pie needs to be completely cool before cutting into it, or it will not be firmed up.