Place the blueberries, sugar, and water in a saucepan and heat over medium heat. Bring to a boil, then cook at a low boil, stirring occasionally, for about 10 minutes until the blueberries break down, mashing them with a wooden spoon or potato masher towards the end of the cook time.
Place the cornstarch in a small bowl and mix with 1 tablespoon water. Add it to the sauce and simmer for about 1 minute, stirring constantly, until thickened.
Remove from the heat and stir in the lemon juice. Taste and adjust sugar as desired. Let the sauce cool to warm; it will thicken even more as it cools. Serve immediately or refrigerate until serving (store up to 1 week refrigerated).