For the Lemon Cordial: In a 4-quart, nonreactive container, combine sugar and lemon peels. Cover and let sit 8 hours (or overnight). The following day, remove and discard lemon peels. Add lemon juice and whisk until sugar is dissolved. Transfer to a Vitamix blender, then blend until incorporated. Strain. Reserve in nonreactive containers or bottles.
To Assemble and Serve: In a Vitamix blender, add all ingredients and 1 cup pebble ice. Blend until smooth. Pour into a glass.
