Place an oven rack in the center of the oven and preheat to 375 degrees F. Butter a 9-inch ceramic or glass pie dish.
For the filling: Finely grind the tapioca in a food processor or spice grinder, about 1 minute. Combine the blueberries, peaches, sugar, lemon juice, vanilla, cinnamon, lemon zest and tapioca in a medium bowl.
Unroll the pie crust and place in the pie dish. Brush the inside with the egg white.
For the topping: Pulse the almonds, butter, oats, flour and sugar until small chunks form in a food processor.
Pour the filling into the crust. Crumble the topping over the filling and bake until the top is golden brown, about 55 minutes. If after 30 minutes of baking the edges of the crust begin to brown too quickly, cover the edges of the pie dish with strips of foil. Cool the pie for 30 to 40 minutes before slicing.