Step 1: Prepare the Pie Crust : In a large bowl, combine flour, salt, and sugar. Cut in chilled butter until mixture resembles coarse crumbs. Gradually add ice water, 1 tablespoon at a time, until dough comes together. Divide dough into two disks, wrap in plastic, and refrigerate for at least 30 minutes. Roll out one disk and fit into a 9-inch pie pan. Trim excess edges.
Step 2: Prepare the Filling : In a large bowl, combine rhubarb, strawberries, sugar, cornstarch, vanilla extract, and lemon juice. Toss gently to coat. Let sit for 10 minutes to release juices.
Step 3: Assemble the Pie : Preheat oven to 400°F (200°C). Pour fruit filling into prepared bottom crust. Dot with butter pieces. Roll out second disk of dough and cut into strips for lattice top. Arrange strips over filling in a crisscross pattern to create lattice. Trim and crimp edges to seal. Brush lattice with beaten egg and sprinkle with sugar.
Step 4: Bake the Pie : Bake for 20 minutes at 400°F. Reduce oven temperature to 350°F (175°C) and bake for 30–40 minutes, until crust is golden and filling is bubbly. Cool on a wire rack for at least 2 hours before slicing.