In a small saucepan over medium heat, combine 1 cup water, the sugar, lavender and mint sprigs. Bring to a simmer and cook until the sugar has dissolved, about 3 minutes. Cool and strain.
In a blender, add the cooled syrup, raspberries and lime juice and blend until smooth.
To serve, place some of the raspberry puree in the bottom of each glass, top with seltzer water and garnish each glass with a sprig of mint.