Combine sugar with 1 ⅓ cups of water and bring to a boil for 5 minutes, or until it begins to thicken. Chill in the refrigerator until completely cold.
Combine the honeysuckle blossoms with 5 ⅓ cups water and allow to steep overnight in the refrigerator.
The next day, combine the honeysuckle solution with the simple syrup and the lemon juice. Add a scant pinch of ground cinnamon. (Smith sticks the point of a sharp knife into the cinnamon and flicks a tiny amount into the mixture.)
Pour chilled mixture into an ice cream maker, following the manufacturer’s instructions to churn.