Add the sugar and the egg whites into a heatproof mixing bowl.
Fit the bowl over a pan of simmering water.
Whisk constantly until the mixture is hot, sugar is dissolved and the egg whites are a little frothy. About 5 minutes. It should look like a shiny marshmallow cream. This step is very important.
With the whisk attachment, transfer to a mixing bowl and beat eggs on medium speed until cooled and thicker for about 5 minutes.
Switch to the paddle attachment and add in one stick of room temperature butter at a time, beating until smooth.
On medium speed, add in the lemon juice and lemon extract.
If the buttercream curdles or separates, just keep beating on high until it comes back together. You should end up with a shiny, smooth and absolutely delicious buttercream frosting!