In a medium saucepan, combine fresh blackberries, granulated sugar, and water. Cook over medium-high heat for about 10 minutes, mashing the blackberries with a fork until they break down. Strain the mixture through a fine mesh sieve into a bowl and let it cool completely.

While the syrup cools, squeeze fresh lemons until you have a generous amount of juice, ensuring there are no seeds. In a large pitcher, combine the freshly squeezed lemon juice with cold water and stir well.

Once the blackberry syrup has cooled, gradually add it to the lemonade base. Start with a smaller amount and taste until you achieve desired sweetness.

To serve, fill glasses with ice and pour the mixture over them. Garnish with fresh blackberries or a sprig of mint.