In a large bowl, whisk together lime juice, oil, and sugar until sugar dissolves.
Dice mangoes and avocados into 3/4-inch cubes; add to bowl. Add green onion, cilantro, chile, and shrimp. Mix very gently. Serve or cover and chill for up to 1 hour. If desired, serve potatoes and corn along side of salad. Serves 6 as first course.