Talk to any southern Italian cook and you'll hear a recipe for salmoriglio. And the odds are they'll all be different. Some add water to the sauce; others go with straight lemon juice. Some cook the sauce gently; others insist it be served without cooking. And so it goes.
I find that both of these steps slightly soften the attack of the oregano, which in my book is a good thing (fresh oregano is about as subtle as raw garlic). The heating also thickens the emulsion a little.
The recipe here is based on one found in "Il Libro d'Oro della Cucina e dei Vini di Sicilia," by Pino Correnti. The main adaptation was reducing the amount of water called for and warming the sauce in a microwave rather than in a double boiler.
Furthermore, rather than whisking the oil into the water and lemon juice to make an emulsion, I find it a lot easier to put the ingredients in a jar, cover it tightly and shake the heck out of it. Works perfectly every time (and is also good for vinaigrette).
Salmoriglio is also good served with grilled swordfish. Cut the fish the Sicilian way, into thin steaks. That way they cook in a flash without drying out.