Drain blackberries and reserve syrup. Set blackberries aside along with 1/4 cup Blackberry syrup. Combine remaining syrup from blackberries and crème de cassis in a medium saucepan and cook on medium-high until juice has reached a low simmer.
Add cornstarch to reserved blackberry syrup, and stir until completely dissolved.
Add cornstarch mixture to simmering syrup, and stir well until liquid is thickened, about 5 minutes.
Add blackberries and lemon juice to thickened sauce and stir until berries are enrobed in sauce.