Juice the lemons and transfer the juice into a large pitcher.

Add the sugar and the water and stir to combine and dissolve the sugar. Add the blueberries and mint.

Using an immersion blender, blend the mixture for about 20 seconds just until the mixture turns pink and the mint is finely chopped. Add alcohol if desired. Let the flavors sit for 1 hour and then pour the mixture into another pitcher through a strainer to remove the blueberry skins and mint leaves.