1. Remove rind from lemons using a vegetable peeler, avoiding white pith; thinly slice rind. Remove pith from lemons; discard. Chop lemon pulp; discard seeds. Combine rind, pulp, cane syrup, 3/4 cup sugar, and salt in a bowl. Cover and refrigerate 24 hours.
2. Preheat oven to 350°.
3. Fit one pie dough circle into a 9-inch pie plate lightly coated with baking spray. Press dough against bottom and sides of pan.
4. Place egg whites and whole eggs in a bowl; lightly beat with a fork to combine. Add egg mixture and butter to lemon mixture; stir to combine. Pour filling into prepared pie plate. Place remaining dough circle over filling; fold edges under, and flute decoratively. Cut slits in top of dough to allow steam to escape. Bake at 350° for 45 minutes or until crust is golden and filling is almost set. Combine remaining 2 tablespoons sugar and 1 tablespoon water. Remove pie from oven (leave oven on); brush sugar mixture over top of pie. Bake at 350° for an additional 5 minutes. Place pie on a wire rack; cool completely before slicing.