In a blender, combine berries, sugar, and lemon juice; blend until smooth. Pour mixture through a fine-mesh sieve, pressing with a rubber spatula to push through. Discard seeds; transfer 1/2 cup berry puree to a small bowl. Cover and refrigerate; reserve for topping.
In a large bowl, combine cream and vanilla; whip until stiff peaks form. Gently fold remaining berry puree into cream. Spoon mixture into custard cups. Cover loosely and refrigerate 1 hour (or up to overnight). To serve, drizzle blackberry fools with reserved berry puree, and garnish with blackberries.