In a small pan stir together two cups of water with the sugar and ginger. Bring the mixture to a boil, stirring until the sugar is dissolved. Simmer it for three minutes. Strain the syrup through a fine sieve set over a bowl and let it cool.
In a jug, combine the cooled syrup, three and a half cups of water and the lemon juice. Stir the lemonade well. Divide the lemonade among tall glasses filled with ice cubes and garnish each glass with a lemon slice.