In a small saucepan mix water, sugar, cornstarch, and salt together. Bring to a simmer and stir until thickened.
Remove from heat. Stir in lemon juice, lemon zest, and fold in mixed berries. Let the filling cool before pouring in the pie. (If you used frozen berries, it will already be cold so you can skip this step.)
Pour the berry filling into an unbaked pie crust rolled out to a 13 inch circle. Top with another pie crust (notes to make a lattice top below). Cut off excess crust and pinch together edges.
In a small bowl, beat together the egg and a teaspoon of water. Brush onto the top of the pie and sprinkle with sugar.
Bake for 45-50 minutes. Allow to sit for at least one hour before serving.
Notes
To assemble a lattice pie crust: Cutting a pie crust into 12-14 strips about 3/4 inches wide. Place 6 evenly spaced across the top of the pie horizontally, Then fold back every other strip and lay one strip vertically. Put horizontal strips back in place and fold back every other strip that was not folded back the first time. Lay a second vertical strip and repeat this process all the way across.