Rinse and dry the apples. Peel 4 apples, cut into quarters, remove the seeds and cut into small pieces. Cut the top off of the other 4 apples to make a lid. With a teaspoon, gently scoop out the pulp and set aside, leaving about a 1.5 cm (approximately 1/2 inch) thick border.
Drizzle the interior of the apple cups and the inside of the lids with lemon juice and refrigerate. Bring the lemon juice of 3 lemons, lemon zest, apple pieces and pulp of the hollowed apples (cored and seeds), water and cinnamon to a boil. Cover and simmer over low heat for 10 minutes. Then pour into a metal bowl and stir in the sugar.
When cool, puree the apple mixture and freeze, stirring every 30 minutes. The sorbet is ready when the desired consistency is reached. Remove the apples from the refrigerator and fill generously with the sorbet. Place the lids on top, dust with powdered sugar and serve immediately.