For the blueberry syrup: Put the blueberries, sugar and lemon juice in a saucepan. Bring to a boil, stirring constantly, then reduce the heat and simmer until thick, 20 to 25 minutes.
Strain the blueberries through a fine-mesh strainer, pressing to get all the liquid out, then place the liquid in the fridge and chill until cold (or place the pan in a bowl of ice to chill down fast).
For the lemonade: Mix the sugar with 6 cups of tap water and stir until the sugar is dissolved to make a simple syrup.
Pour the lemon juice into a large vat. Pour in three-quarters of the simple syrup and 8 cups of water (give or take). Add the blueberry syrup, stir it around and then give it a taste. Add more simple syrup if it needs sweetness, or more water if it needs dilution. Top up with lots of ice before serving.