Step 1: Combine the sugar and egg whites in a medium heatproof bowl and place over a pan of simmering water.
Step 2: Whisk the sugar mixture constantly over heat until the sugar is dissolved and the mixture looks smooth and shiny, about 3 minutes. Remove mixture from heat and pour into a stand mixer bowl. Whisk on medium speed for about 5 minutes until the mixture has cooled.
Step 3: Switch to the paddle attachment and with the speed on low, add the butter a few pieces at a time, beating until smooth. When all the butter has been added, beat the buttercream on medium-high speed for about 6-10 minutes until it is very thick and smooth. Add in the lemon juice and beat until combined. Add in the vanilla.
The buttercream is ready to be used. Place a piece of plastic wrap against the surface until you are ready to use it to prevent it from drying out.