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Combine egg whites, sugar, and salt in the heatproof bowl of a standing mixer set over a pan of simmering water. Whisk constantly by hand until mixture is warm to the touch and sugar has dissolved (the mixture should feel completely smooth when rubbed between your fingertips).
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Attach the bowl to the mixer fitted with the whisk attachment. Starting on low and gradually increasing to medium-high speed, whisking until stiff peaks form. Continue mixing until the mixture is fluffy and glossy, and completely cool (test by touching the bottom of the bowl), about 10 minutes.
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Turn the mixer to medium-low speed, add the butter a few tablespoons at a time, mixing well after each addition. Once all the butter has been added, whisk in vanilla and lemon extracts. Switch to the paddle attachment, and continue beating on low speed until all air bubbles are eliminated, about 2 minutes. Scrape down sides of bowl with a flexible spatula, and continue beating until the frosting is completely smooth.