Make the lavender simple syrup: In a small saucepan over medium-high heat, combine the water and sugar. Bring to a boil. Once boiling, reduce the heat to low and add the lavender. Simmer for 5 minutes, then remove the pot from the heat. Let the lavender steep in the syrup for 10 minutes, then strain into a glass jar. Let the syrup cool completely. The syrup will keep in an airtight container in the refrigerator for up to 10 days.
While the syrup cools, place 2 coupe or martini glasses in the freezer.
Fill a large cocktail shaker halfway with ice. Add the rosemary springs, gin, Meyer lemon juice, 4 tablespoons of lavender simple syrup, and the CBD oil.
Close the shaker tightly and wrap a kitchen towel around it to prevent spilling. Shake vigorously for about 1 minute.
Strain the cocktail into the chilled glasses, dividing evenly.
Garnish each cocktail with a lemon peel and serve immediately.