Blend flour and salt in processor. Add butter and blend, using on/off turns, until mixture resembles coarse meal. Add 2 tablespoons ice water and blend just until dough begins to clump together, adding more ice water by teaspoonfuls if dough is dry. Gather dough into ball; flatten into disk. Wrap in plastic and chill 1 hour. DO AHEAD: Can be made 2 days ahead. Keep dough chilled. Soften slightly at room temperature before rolling out
Roll out dough between sheets of parchment paper to 1/8-inch-thick round, 14 inches in diameter. Remove top sheet of parchment. Using bottom sheet as aid, transfer dough on parchment to large unrimmed baking sheet. Chill 15 minutes.
Preheat oven to 450°F. Combine apple slices, 2 tablespoons sugar, and lemon peel and cinnamon in medium bowl; toss to blend. Arrange apple slices in concentric circles, overlapping slightly. Using parchment as aid, fold plain crust border up over apples, pinching any cracks in crust. Brush crust with milk. Sprinkle crust edges and apples with remaining 2 tablespoons sugar.
Bake galette 20 minutes. Reduce oven temperature to 325°F. Continue baking until crust is golden (cover with aluminum foil if the apples get too brown), about 25 minutes longer. Remove from oven. Slide long thin knife between parchment and galette. Drizzle with caramel sauce and a pinch of sea salt.
Let stand at least 10 minutes. Cut into wedges and serve warm or at room temperature