To make gingerade: Bring 1 cup sugar, 1 cup water, and 1 cup fresh peeled ginger sliced into 1/4-inch pieces to boil in a small saucepan; take off heat to cool. Pour into a blender and puree until liquefied. Strain through a fine strainer and press on the ginger to extract all the syrup. Combine ginger syrup with 1 cup fresh squeezed lemon juice and 3 cups ice cold water in a pitcher. Refrigerate until thoroughly chilled, 30 to 40 minutes.