Whisk the egg yolks and the vinegar briskly in a metal bowl set over a saucepan with about an inch of simmering water at the bottom. If you see even a hint of curdling in the eggs, take the bowl off the heat, but keep whisking. Keep going back and forth from the heat until the mixture turns thick and lightens in color. Whisk in a tablespoon of warm water.
Begin adding the softened butter, a pat at a time. After about a fourth of the butter is in there, you'll begin to see a change in the texture of the sauce. At that point, you can step up the addition of the butter a bit, and keep going till all the butter is incorporated.
Whisk in the cayenne and the lemon juice and serve right away.