Make the crust: In a large bowl, whisk together flour, sugar, and salt. Cut in cold butter using a pastry cutter or your fingertips until mixture resembles coarse crumbs with pea-sized pieces. Drizzle in ice water 1 tablespoon at a time, mixing gently until dough just comes together. Divide into two disks (one slightly larger), wrap in plastic, and refrigerate for at least 1 hour.

Prepare the filling: In a large bowl, combine strawberries, rhubarb, and 1 1/4 cups sugar. Toss gently and let sit for 15 minutes to release juices. Add cornstarch, cinnamon, and lemon juice, stirring until fruit is evenly coated.

Roll out the larger dough disk on a floured surface to a 12-inch circle, about 1/8-inch thick. Transfer to a 9-inch pie plate, letting excess hang over the edges. Refrigerate while preparing the lattice.

Roll out the second dough disk to an 11-inch circle. Using a sharp knife or pastry wheel, cut into 10 strips about 1 inch wide. Place strips on a parchment-lined baking sheet and refrigerate for 15 minutes to firm up.

Pour the filling into the prepared crust and dot with butter pieces. Weave the lattice: lay 5 strips across the pie, then fold back every other strip halfway. Place a perpendicular strip across the center, unfold the folded strips over it, then fold back the alternate strips and add another perpendicular strip. Repeat until lattice is complete.

Trim excess dough to 1 inch beyond the pie plate rim. Fold the overhang under itself and crimp decoratively. Brush lattice with egg wash and sprinkle with coarse sugar.

Place pie on a rimmed baking sheet. Bake at 425°F for 20 minutes, then reduce heat to 375°F and continue baking for 40-50 minutes until crust is deep golden and filling bubbles thickly through the lattice.

Cool completely on a wire rack for at least 4 hours or overnight before slicing. The filling will thicken as it cools.