Peel the rind thinly from the bottom of each lemon, using a potato peeler.
Put these pieces of rind in a saucepan with the water and sugar and heat gently until the sugar has dissolved, then simmer for 10 minutes.
Remove from the heat and leave to cool.
Cut the tops off the lemons and scoop out all the flesh, using a grapefruit knife or pointed spoon.
Put the flesh into a bowl with any juice, reserve the shells and tops.
Remove any pips from the flesh, then puree it in a blender and strain.
Strain the sugar syrup onto the lemon puree and mix well.
Turn into a rigid container, cover and freeze until half frozen.
Trim a little from the bottom of the lemon shells so that they will stand upright.
Put the lemon shells and lids into the freezer to chill.
Whisk the egg white until stiff.
Turn the half frozen lemon mixture into a bowl and whisk until smooth.
Fold in the egg white and then pile the mixture into the lemon shells and put on the lids.
Wrap individually in foil, label and freeze.
When required to serve, unwrap and leave to thaw in the refrigerator for about 30 minutes before serving.