Freeze Ahead: Make sure the ice cream base is in the freezer for at least 24 hours.
Cut + Blend: Remove the seeds and skin from the melon and dice into 1 to 2 inch cubes. You should have 4 to 5 cups of chopped fruit. More or less is fine, you will adjust with the amount of simple syrup you use. In batches, blend the honeydew until it is liquified.
Strain: Strain the honeydew juice through a mesh strainer. Use a spatula to move the solids around without pushing through.
Steep the Syrup: Combine the sugar, water and lavender in a medium saucepan. Bring to a boil over medium-high heat. Boil for 2 minutes, turn off heat and let steep for 5 minutes. Strain out lavender and cool completely.
Build the base: If using the corn syrup, whisk into the honeydew base. Whisk in half the simple syrup then test the base using the egg test. Wash and dry a large egg and lightly float into the base. You want to see a 1-inch circle, about the size of a nickel, of the egg. Too little egg - add more simple syrup. Too much egg - add more honeydew juice or water.
Add the tart: Stir in the lemon juice 1 tablespoon at a time, tasting after each addition until you reach the right acidity.
Chill + Churn: Chill the honeydew lavender sorbet base for at least 1 hour. After completely chilled, pour into the ice cream maker and churn for 10 to 15 minutes.
Freeze: Freeze the churned sorbet a storage container for at least 4 hours. Let soften on the counter for 5 minutes before scooping.
Notes
Replacing ¼ cup of the simple syrup with ¼ corn syrup will result in a 'creamier' smoother and less icy sorbet. After testing both methods, using the corn syrup will produce a texture consistent to store quality sorbet but is still delicious without it.If you can't find fresh lavender, you can purchase culinary lavender at a speciality food shop or Whole Foods. Be sure to use culinary lavender and not the kind you get at the craft store. You probably won't become ill, but why chance it?