Preheat the oven to 180°C/gas 4. Wash the blackberries and remove any leaves and stalks. Peel, core and cut the apples into quarters, then halve again. Put in a large, ovenproof dish and drizzle with the lemon juice. Bake for 15–20 minutes.
Meanwhile, make the topping; place the rolled oats, flour, sugar and butter in a bowl and rub together until well mixed. Gently mix the blackberries and the sugar in with the apple. Cover with the topping and bake for 45 minutes until golden brown. Serve warm with crème fraîche or Greek yogurt.