Preheat your oven to 400 degrees, move the oven rack to the bottom of the oven, and line a 9 inch deep dish pie pan with pie crust. Trim and pinch the edges.
In a large saucepan, combine one cup of blueberries, one cup of strawberries, and one cup of raspberries. Cook over medium heat until the berries cook down, mashing them up with the back of a wooden spoon as you go, about 8 minutes.
In a large bowl combine the remaining uncooked berries, the cooked berries, the sugar, the tapioca, and the lemon juice. Pour into the prepared pie plate.
In a medium bowl with a pastry cutter or two forks, combine the flour, oats, butter, and brown sugar. Sprinkle it over the berry filling.
Line a baking sheet with aluminum foil, set the pie on top of it, and bake for 25 minutes. Turn the temperature of the oven down to 350 degrees and continue baking for 35 to 50 minutes or until the inside of the pie is bubbling and the crust is a deep golden brown. Allow the pie to completely cool before serving.