Soak the gelatine sheets in cold water according to the soaking time specified on the packet.
Wash the limes with hot water and dry them thoroughly. Finely grate the zest from 1 lime. Squeeze the juice from all 3 limes.
Pour about 100 ml of the lime juice into a saucepan, add the grated zest, and heat over medium heat for 2-3 minutes, stirring occasionally, until warm around 60°C (140°F) but not boiling.
Drain the gelatine sheets and add them to the hot lime juice. Stir continuously for 1 minute until fully dissolved.
Separate the eggs. Whip the egg yolks with the sugar and vanilla sugar for 2-3 minutes until pale and creamy.
Slowly pour the warm lime juice mixture into the egg yolks while beating constantly. Refrigerate for 15 minutes until the mixture starts to thicken and gel.
In a clean bowl, whip the egg whites for 2-3 minutes until stiff peaks form. In another bowl, whip the cream for 1-2 minutes until stiff peaks form.
Fold the whipped egg whites gently into the lime mixture, then fold in the whipped cream.
Refrigerate for 2 hours until fully set. Garnish with lemon balm just before serving.