Heat a small, heavy skillet on medium and toast coconut for 3–4 minutes, stirring often, until it becomes a toasty brown. Cool in a saucer.
Combine lime juice, fish sauce, and sugar in a salad bowl; stir until sugar dissolves and mixture forms a smooth sauce. Add citrus fruit, toasted coconut, peanuts, shallots, chiles, and mint or cilantro. Toss gently with your hands until mixture it thoroughly combined.
Line a serving bowl or platter with lettuce leaves and pile the salad into the middle. Serve at room temperature to maximize flavors.