Put the water, ginger and sugar into a saucepan over medium heat. Using a vegetable peeler, peel off the lemon zest in several large strips, avoiding the white pith beneath, and add the zest to the pan. Squeeze the lemon juice into the pan and stir to combine.
Bring to a boil, then remove the pan from the heat, cover with a lid, and let sit for 30 minutes. Strain the syrup into a clean container and discard the solids.
To make each drink, fill a tall glass with ice and add the cranberry juice and seltzer. Stir in 3 tablespoons of the ginger syrup.