Mix together sugar, 1/2 cup tapioca flour, and salt in a bowl.
Pour 3/4 of the sugar mixture on the strawberries, add 1 tablespoon extra tapioca flour, and vanilla extract. Stir to combine very well. Set aside for 10 minutes to macerate.
Pour the remaining 1/4 of the sugar mixture on the blueberries and add lemon zest and lemon juice. Stir to combine well. If the mixture seems very dry, smash a few blueberries to allow the mixture to coat the blueberries better.
Add in a bit more sugar to the berries, if necessary, depending on the sweetness of your fruit.
Once the strawberries have macerated (softened and produced juice), sprinkle in the remaining 1 tablespoon of tapioca flour and stir to mix very, very well (see note).
Fold a piece of aluminum foil in half width-wise a couple times to make a divider for the fruit. Put the foil inside the pie crust blocking off a third of the inside of the pie (see photo).
Spoon blueberries into the smaller side. Then, using a slotted spoon, spoon strawberries into larger side, leaving strawberry liquid in bowl. Carefully remove the foil.
Roll out smaller ball of dough and cut out a few strips, about 3/4-1” thick. Slide a kitchen knife under the crust strips (above the parchment paper) and lift up to remove. Place over strawberry section to resemble American flag. Cut out stars with cookie cutter and place over blueberry section. Use your fingers or a kitchen knife to easy away the dough around the star, then slide the knife under the star and lift up. Be very gentle, as this dough can be delicate.
In a small bowl, combine whisked egg with 1 teaspoon water. Using a pastry brush, gently brush the top crust and bottom crust edges with the egg wash. Bake for 25-30 minutes uncovered, or until top crust is golden brown. Cover edges or entire pie (depending on how brown the stars and stripes are) and bake another 5-10 minutes, or until filling is bubbly and crust is golden brown. Remove from oven and let cool at least 2 hours before cutting. Perfect with coconut ice cream!