In a medium saucepan, stir together 1 cup water and the fresh raspberries. Heat over medium low heat for 5 minutes. Drain the water and return berries to pan.
Stir in remaining 2 1/2 cups water. Whisk in sugar, cornstarch, and salt. Heat over medium heat to reach a boil. Stirring constantly, cook mixture for 5 minutes until thickened.
Remove from heat and stir in fresh lemon juice. Allow to cool to room temperature. Transfer to a plastic container and refrigerate at least 3 hours, or overnight. Serve in dishes topped with whipped cream and reserved blackberries.