In a medium saucepan, combine the blackberries, sugar, and 1 cup of water. Stir gently to mix the ingredients evenly.
Place the saucepan over medium heat. Using a fork or potato masher, gently mash the blackberries as they warm. Continue this process until the berries burst and release their juices, and the mixture begins to simmer.
Introduce the fresh sage leaves into the saucepan. Allow the mixture to simmer for an additional 5 minutes, which will infuse the syrup with the aromatic flavor of the sage.
Remove the saucepan from the heat. Using a fine-mesh sieve, strain the blackberry-sage syrup into a bowl, pressing down on the solids with the back of a spoon to extract as much liquid as possible. Discard the remaining solids.
In a large pitcher, mix the strained syrup with the freshly squeezed lemon juice and the remaining 3 cups of water. Stir thoroughly to ensure all components are well integrated.
Taste the lemonade and feel free to adjust the balance of sweetness and tartness by adding more sugar for sweetness or lemon juice for tartness according to your personal preference. Allow the mixture to chill in the refrigerator for at least 30 minutes to enhance the flavors.
To serve, fill glasses with ice cubes and pour the chilled lemonade over the ice. Garnish each glass with a lemon slice and a sprig of fresh sage for a refreshing presentation.