With an electric mixer, cream butter and sugars until light, scraping down sides of bowl as needed. Add lime zest, lime juice, and salt; beat until combined. Add flour; beat until dough is just combined.
Place dough on a 16-by-12-inch piece of parchment or wax paper. Using your hands, shape into an 8-inch log; flatten into a rectangle (1 1/2 inches high and 2 1/2 inches wide). Fold paper over log; flatten sides against work surface. Refrigerate dough until firm, at least 1 hour and up to 1 day.
Preheat oven to 350 degrees. Line two baking sheets with parchment. Slice dough crosswise 1/4 inch thick; place on sheets. Bake, rotating sheets halfway through, until cookies are puffed and barely golden, about 15 minutes. Transfer to a wire rack to cool; glaze.
To make Lime Glaze: In a small bowl, whisk together all ingredients until spreadable. Using back of a small spoon, spread about 1/2 teaspoon glaze on each cooled cookie.