Combine the sugar and water in a medium saucepan set over medium heat. Bring to a boil and use a wooden spoon to stir occasionally until the sugar is completely dissolved, about 2 minutes. Turn off the heat and set the simple syrup aside to cool for 5 minutes.
In a blender jar, combine the ginger and sliced lemon; add the warm simple syrup and place a lid on the blender. Begin blending on the lowest speed until the ginger and lemon are roughly chopped, about 1 minute. Turn off the blender and let the ginger-lemon syrup steep for 10 minutes. Repeat, this time blending the ginger-lemon syrup on medium speed for 1 minute before turning the blender off and steeping for 10 minutes more.
Strain the ginger-lemon syrup through a fine-meshed sieve lined with 2 layers of water-moistened cheesecloth, set over a medium bowl, using a rubber spatula to help push the mixture through.
Fill a glass with ice, add 3/4 cup seltzer water. Top with ¼ cup ginger-lemon syrup and use the spoon to stir. Adjust the flavor with more ginger-lemon syrup or seltzer as needed. Garnish with a lemon wheel.
The remaining ginger-lemon syrup can be stored in an airtight container for up to 1 week.