For the Lemon Curd: Combine the sugar, lemon juice, and eggs in a bowl and cook over a double boiler, whisking constantly until the mixture reaches 80°C / 175°F.
Take off the heat and transfer to a mixer bowl. Whip on high speed and add the butter in small pieces. Whip until the curd has cooled to room temperature.
Reserve at room temperature if the Italian meringue is to be made immediately after; otherwise, refrigerate immediately.
For the Meringue: Place the sugar in a saucepan with about one-quarter of its weight in water or enough to obtain a wet-sand texture. Make sure there are no sugar crystals along the inside of the pot and that all the sugar has been hydrated.
Begin whipping the egg whites and cream of tartar on medium speed at the same time that the sugar begins cooking.
Cook the sugar to 121°C / 250°F (also known as the soft ball stage).
When the sugar has reached 115°C / 240°F, increase the speed of the mixer to high.
When the sugar reaches 121°C / 250°F, take the pot off the heat.
Wait for the egg whites to reach stiff peak, and immediately after pour the sugar down the side of the bowl and whip until the foam has cooled to room temperature.
For the Lemon Chiboust: Fold the Italian meringue gently into the lemon curd. If the curd was refrigerated, it needs to be warmed up slightly in order to fold into the meringue smoothly. Pour into a piping bag. Reserve under refrigeration until needed.