Chill butter for 15 minutes. In a bowl, combine flour, sugar, and salt. Cut in butter until it resembles coarse crumbs. Gradually add ice water until dough forms. Shape into a disk, wrap, and refrigerate for at least 2 hours.

Preheat oven to 375°F (190°C). Roll out dough to 1/8 inch thickness and fit into a rimmed baking sheet.

In a bowl, combine strawberries and blackberries with sugar and lemon juice. Mix gently while avoiding excess liquid.

Spread berry filling over the rolled-out dough. Roll out another portion of dough for the top crust.

Brush top crust with egg wash and sprinkle with sugar. Bake for 50 minutes until golden brown.

Let pie cool on a wire rack for 30 minutes. Serve warm or at room temperature.