For the jalapeno-berry syrup: Put the blueberries, raspberries, blackberries, sugar, jalapenos and lemon juice in a saucepan. Bring the mixture to a boil, stirring constantly, and then reduce the heat and simmer until thick, 20 to 25 minutes.
Strain the mixture through a fine-mesh strainer and press on the fruit with a wooden spoon to get all of the liquid out. Set the berry syrup aside to cool.
For the simple syrup: Mix the sugar with 6 cups water and stir until the sugar is completely dissolved.
For the lemonade: Pour the jalapeno-berry syrup and lemon juice into a large vat. Add 6 cups of the simple syrup and 8 cups of cold water and stir to combine. Top up the container with plenty of ice before serving.