Step 1

Roll out a disk of dough on a lightly floured surface to a 13" round. Transfer round to a parchment-lined baking sheet and chill while you roll out remaining disk of dough to a 13" round (about ¼" thick). Cut second round into 4 strips, about 2 ¼" wide. Stack strips on top of first round of dough, separating with a sheet of parchment. Chill while you prepare filling.

Step 2

Preheat oven to 350°. Combine granulated sugar, cornstarch, and salt in a large bowl. Add strawberries, lemon slices, and vinegar. Toss to coat fruit evenly in sugar mixture, separating lemon slices that stick together.

Step 3

Beat egg with 1 tsp. water in a small bowl just to blend. Lift parchment with strips of dough onto work surface. Using your hands, or wrapping dough around a floured rolling pin if you're nervous, carefully transfer round of dough to a 9" pie dish. Lift up edges and allow dough to slump down into dish. Trim edges of dough with kitchen shears to even out, leaving at least a 2" overhang (or, you can leave untrimmed if you want a rustic look); brush edge with half of egg wash. Scrape in strawberry filling along with any accumulated juices in bowl.

Step 4

Lay 2 strips lengthwise over pie filling, then arrange remaining 2 strips crosswise across pie, working alternately over and under lengthwise strips to create a lattice pattern. Fold edge of bottom round up and over strips and press to seal. Brush dough with remaining egg wash; sprinkle with demerara sugar.

Step 5

Place pie pan on a foil-lined rimmed baking sheet (juices may bubble over—this is what the foil is for). Bake until crust is deep golden brown on top and bottom and juices are bubbling, about 1 ½ hours. Transfer pie to a wire rack and let sit at least 4 hours before slicing.

Step 6

Do Ahead: Pie can be made 2 days ahead. Cover and chill.