Add blackberries, the 1 tablespoon of water, sugar and zest to a small pan. Heat over low for three to four minutes, gently stirring until the blackberries have given off juices, the sugar is melted and mixture simmers. When blackberries have reached your desired stage (they can be cooked until just soft or cooked longer if you wish them to break apart) add the cornstarch slurry. Mix; the sauce should start to thicken immediately. Remove from heat. The sauce will be thicker once cooled.
Mix the slurry:
Mix together lemon juice and water. In a small cup, add the cornstarch. Slowly while stirring, add in the lemon juice water mixture into the cornstarch. If this mixture sits, the cornstarch will thicken on the bottom of the cup. Just stir together before using.