In a small saucepan, combine blackberries, sugar, and water over medium heat.
In a small bowl, whisk together cornstarch and lemon juice.
Stir cornstarch mixture into the saucepan.
Bring to a gentle simmer, stirring frequently, until sauce thickens (about 5–7 minutes).
Remove from heat. Let cool before serving over cheesecake.
Notes
Sauce thickens more as it cools. - For a seedless version, strain through a fine mesh sieve. - Can be made ahead and stored in the fridge for up to 5 days.