Peel off the lemon rind with a vegetable peeler, making sure you leave behind the pith (the white part). Set the lemon rind aside. Store the lemon, covered, in the fridge for another use.
Combine the still/tap water, sugar, ginger, lemon rind, and 2 rosemary springs in a small saucepan over medium-high heat. Stir continuously until the sugar dissolves and the mixture comes to a boil. Let boil 3 minutes, then remove pan from heat.
Let simple syrup ingredients steep for one hour.
Place a small strainer over a glass jar or container, then pour the syrup through the strainer. Discard the cooked lemon rind and rosemary sprigs.
Refrigerate the spruce simple syrup until you’re ready to make the spruce soda.