In a nonreactive pot, such as enameled or stainless steel, whisk together sugar and salt. Whisk in whole egg and yolks, then immediately whisk in lemon zest and juice.
Place pot over medium heat and bring mixture to a simmer, whisking constantly, until bubbling in center and thickened, about 5 minutes.
Remove from heat and whisk in butter. (For a thicker consistency, use 4 tablespoons; for thinner—say, for use as a sundae topping—use 3 tablespoons.)
Strain through a fine-mesh sieve set over a bowl, to remove any zest and cooked pieces of egg white.
Press a piece of plastic wrap directly on surface and let cool completely, about 20 minutes.
Refrigerate until thickened and cold, at least 1 hour or, in an airtight container, up to 1 week (or freeze in an airtight container up to 2 months).