Heat oven to 350 degrees. Slice the mangoes into 3/4-inch pieces; transfer to a medium bowl. Stir in the lemon juice, 3 tablespoons sugar, and 1 tablespoon flour, and set aside.
In a medium bowl, whisk together hazelnuts, salt, remaining 3/4 cup flour, and 1/3 cup sugar until combined. Cut in butter with a pastry cutter or two knives, until the mixture is crumbly. Continue working in the butter until completely incorporated and there are no dry crumbs. Squeeze mixture together to create pea-size to half-inch clumps.
Add the raspberries to the reserved mangoes, and divide the mixture among four small baking dishes. Place one-quarter of the nut-and-flour mixture on top of each baking dish, allowing some of the fruit to show through. Bake until top is golden brown and the fruit juices are thick and bubbling, 35 to 40 minutes. Remove from oven; place on a wire rack until slightly warm.
Store up to one week in the refrigerator.