Whisk flour, sugar, and salt together in a large bowl. Cut in cold butter with a pastry cutter until mixture resembles coarse crumbs with pea-sized bits of butter remaining. Do not overwork.
Stir vinegar into ice water, then drizzle over flour mixture one tablespoon at a time, tossing with a fork. Add just until dough clumps together when squeezed.
Divide dough in half, shape each into a flat disc, wrap in plastic, and refrigerate for at least 1 hour or up to 2 days.
Peel, core, and slice apples uniformly. Place in a large bowl with sugars, cornstarch, cinnamon, nutmeg, salt, and lemon juice. Toss until well coated. Let sit at room temperature for 15-20 minutes.
Roll one dough disc into a 12-inch circle, about 1/8-inch thick. Transfer to a 9-inch pie plate, press gently into bottom and sides without stretching. Trim excess to a 1/2-inch overhang. Chill while preparing lattice.
Preheat oven to 425°F with a baking sheet on the lower rack. Roll second dough disc to 12 inches. Cut into 10-12 strips, each about 3/4-inch wide, using a fluted pastry wheel or knife. Chill strips on parchment for 10 minutes if soft.
Stir apple mixture and pour into chilled bottom crust, mounding slightly in center. Dot with pieces of butter.
Lay half the strips evenly across the pie in one direction. Fold back every other strip, lay a perpendicular strip across, then unfold. Repeat, alternating folded strips, to weave the lattice across the entire top.
Trim excess lattice strips even with bottom crust overhang. Fold bottom crust up and over the lattice ends, pressing to seal. Crimp the edge decoratively.
Whisk egg with water or cream. Brush egg wash over the lattice and crimped edge. Sprinkle with turbinado sugar. Refrigerate assembled pie for 15-20 minutes.
Place pie on the preheated baking sheet and bake at 425°F for 20 minutes. Reduce temperature to 350°F and bake for 35-40 minutes more, until crust is golden and filling is bubbling in the center. Cover edges with a pie shield if browning too quickly.
Cool on a wire rack for at least 3 hours before slicing to allow the filling to set. Serve warm, at room temperature, or chilled with ice cream or whipped cream.