In a large sauce pan on medium heat, heat the cherries with both sugars. The cherries will release a lot of water. Stir to keep the cherries on the bottom from scorching. Some of the smaller cherries might break down. Cook for 10 minutes. While the cherries are cooking make a slurry with the lemon juice and cornstarch. Add the cornstarch slurry to the cherries and bring to a boil. Cook until the mixture thickens.
Remove from the heat and transfer to a mixing bowl and cool to room temperature.
Preparing the crust
While the filling is cooling roll out one of the disks of dough into a thin circle. Line the pin pan and place back in the refrigerator to cool.
Assemble the pie
Preheat the oven to 350°F or gas mark 4.
Remove the pie pan from the refrigerator along with the other disk of dough. Fill the pie pan with the filling and top with either a lattice or the other disc of thinly rolled dough. If you are not using a lattice make sure to cut vents into the top of the dough. Trim the dough and style the edges as desired.
Place the pie on the lined cookie sheet. Cook for an hour or until the crust is golden brown. Remove and let cool before slicing.