Combine ginger (don't bother to peel it), sugar, and 1 1/2 cups water in a medium saucepan and bring to a boil, stirring to dissolve sugar. Lower heat and simmer mixture about 15 minutes, or until it reaches the consistency of pancake syrup (you should have about 1 cup syrup).
Strain syrup and cool to room temperature. Stir in lemon juice.
Place 2 tablespoons syrup in each of eight 8-ounce glasses and fill three quarters full with club soda. Gently stir to blend. Add ice and more club soda or syrup if necessary.