Preheat oven to 350 degrees F. Slice the rind off the top of the brie, leaving a ½-inch border along the edges. Place on a parchment-lined baking sheet and bake for 12 to 15 minutes, or until the cheese is beginning to melt.
Meanwhile, heat the water, sugar and lemon juice over medium heat in a small saucepan. Stir until the sugar dissolves, then allow the mixture to boil until it is reduced to about 2 tablespoons.
Pour the syrup into a blender with 1 cup of the blackberries and puree until smooth. Press the puree through a fine-mesh sieve set over a small bowl to remove the seeds. Stir the remaining blackberries into the sauce.
Using a large, flat metal spatula, transfer the brie to a serving platter and top with the blackberry compote. Serve with your favorite crackers or baguette slices.