Bring 450 ml water and sugar to the boil, simmer briefly. Let the syrup cool down.
Wash the organic lemon and cut off 4 slices. Squeeze juice from all lemons and measure 200 ml. Mix syrup and juice in a metal bowl. Put in the freezer for 30-45 minutes. Wash lemon balm and chop leaves from 4 stems.
Beat the egg white until stiff, stir into the ice cream mixture with lemon balm. Freeze for another 4 hours, stirring vigorously more often.
Cut the melon into slices, remove the seeds and cut the flesh from the skin. Add apple juice, puree everything finely.
Shape the sorbet into 8-12 balls. Freeze again for at least 30 minutes. Arrange the sorbet and melon sauce in pre-cooled glasses with 1 slice of lemon each. Decorate with the rest of the lemon balm. If necessary, add the rest of the sauce separately.