Heat the sugar and 1 cup water in a small pot until the sugar has dissolved and the liquid just comes to a boil. Turn off the heat and add the ginger. Let cool, then strain the syrup into a large mason jar and discard the ginger. Add the lemon juice to the syrup and refrigerate until ready to use.
Fill 4 large glasses with ice, pour 1/4 cup of the syrup into each glass and top up with some club soda. Add a slice of lemon to each glass and serve.