Preheat the oven to 375°F (190°C).
In a mixing bowl, combine the mixed berries, granulated sugar, and lemon juice. Toss to coat the berries in the sugar and lemon juice mixture.
In a separate bowl, combine the flour, cocoa powder, brown sugar, ground cinnamon, and salt. Mix well.
Add the cold butter to the flour mixture. Use your fingers or a pastry cutter to cut the butter into the flour until the mixture resembles coarse crumbs.
Stir in the semisweet chocolate chips.
Pour the berry mixture into a baking dish. Sprinkle the chocolate crumble evenly over the top.
Bake in the preheated oven for 35-40 minutes, until the berries are bubbling and the crumble topping is golden brown.
Remove from the oven and let cool for a few minutes before serving.
Serve warm with a scoop of vanilla ice cream, if desired.