Place lemon peel and vodka in a large airtight container and let steep, undisturbed, in a cool, dark place for 5 to 7 days. Strain vodka into a new container. Place sugar and water in a medium pot over medium-high heat; heat, stirring occasionally, until sugar dissolves. Remove from heat and cool completely. Strain vodka mixture into a clean, large airtight container, discarding lemon peels. Stir in simple syrup until combined. Cover and store in the refrigerator.