1. On a flat plate, mix 1/4 cup of the sugar with cinnamon.
2. Stack tortillas, and with a small knife, notch edges to make sunburst rim; reserve scraps for other uses. Cut tortillas in half, rub sides lightly with water, and coat, 1 piece at a time, with cinnamon sugar. Arrange pieces in a single layer on 2 baking sheets (12 by 15 in.).
3. Bake in a 400° oven until tortillas are lightly browned and crisp, about 10 minutes; switch pans halfway through baking.
4. Meanwhile, peel and pit mango. Seed and peel melon. Cut mango and melon into 1/2- to 3/4-inch cubes, or cube half of each and thinly slice remainder. Mix fruit with lemon juice.
5. Arrange fruit equally on salad or dessert plates.
6. In a 6- to 8-inch frying pan over high heat, melt remaining 1/4 cup sugar, shaking and tilting pan to mix dry sugar into syrup until liquid is amber color; remove from heat. At once, put frozen yogurt beside fruit, lean tortillas against frozen yogurt, and quickly drizzle desserts with melted sugar.