You can remove the skin of the ginger by scraping with a spoon, but it is ok to leave the skin on too! In a medium saucepan, combine 2 cups of the water with the ginger, and simmer over medium heat for 20 minutes.
Stir in the lemon juice and honey and let cool completely. Strain the ginger mixture into a large pitcher, and add the remaining 6 cups of water. Add the ice cubes, and let stand until well chilled before serving.