Place butter and sugar in a large bowl; beat with a mixer at medium speed for 5 minutes or until light and fluffy.
Add egg, 1 tablespoon lime rind, and lime juice; beat 2 minutes or until well combined.
Lightly spoon flour into dry measuring cups; level with a knife.
Combine flour, baking powder, and 1/8 teaspoon table salt; stir with a whisk.
Add flour mixture to butter mixture, and beat just until combined.
Divide dough into 2 equal portions. Shape each portion into a 6-inch log. Wrap logs individually in plastic wrap; chill 3 hours or until firm.
Preheat oven to 350°.
Cut each log into 16 (about 1/3-inch-thick) slices, and place 1 inch apart on baking sheets lined with parchment paper.
Sprinkle the cookies evenly with remaining 2 teaspoons lime rind, turbinado sugar, and sea salt.
Bake at 350° for 10 minutes or until edges are lightly browned.
Cool for 2 minutes on pans on a wire rack. Remove from baking sheets, and cool completely on wire rack.