In a medium saucepan bring 1 cup of water to a boil and add ginger. Reduce heat to medium low and let ginger simmer for 5 minutes. Remove the pan from heat and let sit for 20 minutes to cool.
Pour liquid into a blender and blend until smooth then strain the liquid through a fine mesh strainer. Set aside.
In a small saucepan boil the remaining 1/2 cp. water and stir in the sugar to dissolve to make a simple syrup.
Pour equal amounts of the ginger water and simple syrup into 2 glasses.
Squeeze juice from 1/2 lemon into each glass and stir.
Top with sparkling water.
Serve over ice and garnish with a lemon slice (optional)