De-seed the melons and scoop out 20 balls from each of the melons and set to one side.
Cut the remaining melon flesh into small pieces and puree together with the lemon juice and apple juice.
Sweeten according to taste.
Pour the sorbet mixture into a flat metal bowl and place in a freezer for ca. 3 hours, stirring well every 20-30 minutes with a fork to prevent large ice crystals forming.
Scoop the sorbet into chilled glasses, garnish with the melon balls and lavender sprigs and serve immediately.