Combined the sugar, water and ginger in a small pot and bring to a boil over medium-high heat. Let the sugar dissolve but not caramelize.
While the sugar water comes up to a boil, squeeze the lemons into a pitcher, discarding the seeds and rind. Add ice to the lemon juice until it comes about halfway up the sides of the pitcher. Strain the ginger-infused sugar syrup into the lemon juice then top it off with some water.