Dice tomatoes. Stir together lime juice and next 2 ingredients until blended.
Pour oil to depth of 2 inches into a Dutch oven; heat to 375°. Fry okra, in batches, 7 to 10 minutes or until crispy and deep golden brown; drain on paper towels.
Toss together shallots, next 2 ingredients, okra, tomatoes, 3 Tbsp. lime juice mixture, and red pepper to taste in a large bowl. Sprinkle with mint and cilantro. Serve with Yogurt Sauce and remaining lime juice mixture.