Squeeze the lemons. Put 150 g sugar, half lemon juice and 150 ml water in a small pot, bring to the boil and simmer for about 5 minutes. Leave to cool.
Wash the basil, remove the leaves. Add remaining lemon juice and basil leaves to the syrup. Puree everything finely. Pour the mixture into a flat, freezer-proof bowl. Freeze covered with foil for about 1 hour.
Beat the egg whites until stiff and carefully fold the beaten egg white into the frozen liquid. Then freeze for a further 4 hours, stirring with a fork every 30-45 minutes to make a fine sorbet.
Form balls from the sorbet mass with the ice cream scoop or tablespoon. Freeze on a plate covered with baking paper for about 1 hour. Then arrange the sorbet in pre-cooled glasses.