In a food processor, purée 2 cups (500 ml) of the frozen papaya (keep the remaining pieces for another recipe) with the remaining lime juice and the sugar until smooth and silky. Use a spatula to scrape down the sides of the food processor as needed. Fill the papaya bowls with the sorbet. Garnish with the small dice of fresh papaya, dried papaya, poppy and chia seeds, and lemon balm leaves.