Preheat the oven to 425º (220ºC).
Combine the strawberries, cherries, sugar, flour, and lemon juice in a deep bowl. Give it a stir to mix well, then set aside so the fruit can release its juices.
Meanwhile, lightly flour a counter or cutting board. Roll one of the pie crusts into a 10-inch (25-cm) circle. Fit it into a 9-inch (22-cm) pie plate, letting the crust hang over the sides—don’t trim it just yet.
Roll out the second pie crust into a 9-inch (22-cm) circle.
Stir the filling, and spoon it into the pie plate. Cover with the remaining rolled out pie crust. Use a scissor to trim the edges, and flute them, or crimp closed with the tip of a fork. Brush the top with the egg wash. Use the tip of a sharp paring knife to slit vents in the top (or a small round cookie cutter works, too).
Bake for 15 minutes, then reduce oven temperature to 350º (180ºC). Bake for 30 to 35 minutes more, until the crust is golden, and juices begin to bubble from the pie. Transfer to a wire rack, and let cool completely, at least 4 hours, before serving.