Slice bananas and cook to a purée with the granulated sugar and water (5–10 min.). Add strained lemon juice and beat to a smooth cream. Boil the milk, sprinkle in the tapioca and cook gently for about 15 min., stirring all the time. Add banana purée, taste and re-sweeten if necessary. Whisk egg whites stiffly and fold lightly into the banana tapioca mixture. Stir lightly until cool and serve piled up in a glass dish. Chill if liked.