Squeeze the lemons. Measure out 300 ml of juice. Heat lemon juice, 200 ml water, sugar and grappa and stir until the sugar is dissolved. Leave to cool. Pour into a bowl. Freeze in the freezer, stirring several times at intervals. Halve the melons.
Remove seeds with a spoon. Cut out the flesh with a ball cutter. Put the melon halves in the freezer for about 1 hour. Scrape off fruit ice cream with a spoon. Pour the melon balls into the melon halves. Serve garnished with lemon balm