Whisk sugar, flour, and salt with a mixer on low speed. With the machine running, add lime and lemon juices, and then butter, in a slow, steady stream, and whisk until well combined. Add lime and lemon zests, raise mixer speed to medium, and whisk for 2 minutes. Transfer to a nonreactive container, cover, and refrigerate overnight (or up to 1 week).
Preheat oven to 350 degrees. Spoon 2 teaspoons batter into mounds on an unrimmed baking sheet lined with a nonstick baking mat, spacing at least 2 inches apart. Using an offset spatula, spread mounds into thin, even circles. Bake, rotating pan halfway through, until golden 10 to 12 minutes. Let tuiles cool slightly on sheet for a few minutes. (They should stay warm and flexible.) Drape each round, smooth side up, into a fluted 2 1/2-inch-wide, 1-inch-deep tart mold to form a flower shape. If flat rounds harden before you drape them, reheat in oven until pliable, about 30 seconds. Let flower-shaped tuiles cool until hardened. Store until ready to use (up to 1 day).
Make the curd: Whisk egg yolks and sugar in a large heatproof bowl set over a saucepan of simmering water, until thick ribbons form when mixtures falls from whisk, about 5 minutes. Add lime zest and juice, butter, and salt, and whisk until butter melts and mixture is well combined. Cook, stirring occasionally, until thick enough to coat the back of a spoon, about 30 minutes. Strain through a fine sieve into a bowl.
Press plastic wrap directly on the surface of the curd. Refrigerate curd overnight. Freeze in an ice cream maker according to manufacturer's instructions until pale and doubled in volume. Transfer to an airtight container, and freeze at least 1 hour (or up to 3 days).
Just before serving, scoop a 1 1/2-inch ball of frozen curd into the center of each tuile. Garnish with sugared flowers, and serve immediately.