Preheat oven to 350º F. Lightly grease six 4-inch ramekins or one 10-inch pie dish.
In a medium bowl, whisk oats, flour, brown sugar, spices, and salt to combine. Toss in butter to coat. With a pastry blender or clean fingers, work butter into the dry ingredients until the mixture is crumbly and the butter is evenly distributed. Set aside.
Prepare the fruit filling in a separate medium bowl. Whisk brown sugar, flour, and salt together, smashing or removing any hard clumps of brown sugar in the mixture. Add blackberries, lemon zest and juice, and stir until combined.
Spoon filling into ramekins or pie dish. Sprinkle crisp topping evenly over the filling. Bake until the fruit bubbles thickly and the crisp topping is golden, about 40 to 45 minutes.
Serve warm with vanilla ice cream and fresh berries.