In a food processor/blender, combine the sugar and lavender petals and blend until the lavender turns to a fine powder. Empty into a bowl and set aside.
Heat the cream and 2 cups of coconut milk in a medium saucepan over medium heat. Bring it to a high simmer but not a boil.
In the food processor/blender, blend the remaining 2 cups of coconut milk with the sugar and lavender mixture, salt, and arrowroot powder.
Add the lavender milk mixture to the saucepan and whisk to combine well. Continue to stir occasionally until the milk mixture is thick and sticks to the back of a spoon.
Place the blueberries in the food processor/blender and blend until you have a blueberry puree.
Remove the saucepan from the heat and stir in the blueberry puree, vanilla, and lemon juice. Strain the mixture into a large glass storage container and let cool. Once cool, cover and refrigerate overnight.
The next day, whisk the gelato mixture, pour into an ice cream machine, and churn it according to the manufacturer’s directions. (Mine took about 20 minutes to churn.)
Notes
Before you start: This recipe requires an ice cream maker. Be sure to have your ice cream maker barrel frozen before making this recipe. I use my machine on the gelato setting.