Combine the syrup, lemon juice, lemon zest, and mint in a small pitcher. Place in the refrigerator to chill.
Shave the ice by placing 2-3 handfuls of crushed ice at a time in a food processor and running the machine until the ice is finely shaved. Store shaved ice in a large re-sealable plastic bag in the freezer for up to one day.
Place a glassful of shaved ice in a serving dish. Pour 3 to 4 tablespoons of the syrup mixture over the ice. Serve immediately.