Preheat oven to 375 degrees. In the bowl of an electric mixer fitted with the paddle attachment, combine 1 cup flour, brown sugar, cinnamon, salt, and oats. Mix on low for 30 seconds, add butter, and mix until clumps form, 4 to 5 minutes. Transfer to a bowl, cover, and refrigerate until ready to use.
Peel and pit nectarines, and cut into 1-inch chunks; place in a large bowl. Halve mangoes lengthwise, angling the knife slightly to cut around the pit. Remove and discard pit and peel. Cut flesh into 1-inch chunks, and add to nectarines; add raspberries. Add remaining 1 1/2 tablespoons flour, granulated sugar, and lime juice; toss gently to combine.
Transfer fruit to a shallow 12-inch round gratin dish. Distribute topping evenly over fruit. Bake until topping is golden brown and juices bubble, about 50 minutes. Remove from oven, and let cool slightly. Serve warm with ice cream.