Pour 7 cups of warm water into the pitcher and put the green tea bags into the water. Drop the piece of ginger into the pitcher. Allow to steep while preparing the simple syrup.
In a 1 quart saucepan, simmer 1 cup of sugar and 1 cup of water until the sugar has dissolved. Remove from the heat and allow to cool for 5 minutes.
Remove the tea bags from the pitcher and add the lemon juice. The ginger can remain in the pitcher as it will continue to flavor the tea.
Stir in the simple syrup.
Fill the pitcher with ice and refrigerate for at least 15 minutes before serving.