In a mixing bowl, combine flour, salt, and sugar for the pie crust. Cut in the chilled butter until the mixture resembles coarse crumbs.
Gradually add ice water, a tablespoon at a time, mixing until the dough comes together. Divide the dough in half, shape into disks, wrap in plastic wrap, and refrigerate for at least 1 hour.
Preheat oven to 425°F (220°C).
Roll out one disk of dough on a floured surface to fit a 9-inch pie dish. Place the crust into the dish and trim any excess.
In another mixing bowl, combine sliced strawberries, chopped rhubarb, sugar, cornstarch, vanilla extract, lemon juice, and cinnamon. Stir until the ingredients are well mixed.
Pour the filling into the prepared pie crust. Dot the filling with small pieces of butter.
Roll out the second disk of dough and cut into strips to create a lattice top or simply cover it with the dough. Seal the edges and cut slits for steam to escape if using a full crust.
Bake in the preheated oven for 15 minutes, then reduce the temperature to 350°F (175°C) and continue baking for an additional 30 minutes, or until the filling is bubbly and the crust is golden.
Let the pie cool for at least 1 hour before serving to allow the filling to set.