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.