Preheat barbecue or broiler.
Place olive oil and juice and zest of 3 lemons into a small saucepan and place over medium heat. Bring to a near boil, remove from heat and pour into a bowl. Immediately add the marjoram "brush" and limoncello and allow to steep, like tea, for 1 hour, covered. This mixture can be stored in a lidded jar, away from light, for up to a week.
Kill lobsters by piercing their shells with a sharp point at the center of the back end of the eyes. Place the whole lobster on the hottest part of the grill for 3 minutes per side and remove from the heat. Cut the lobsters in half lengthwise and, careful not to lose a drop of the tomalley or roe, gently anoint them with the scented oil, using the marjoram brush. Gently place them, shell-side down, on the grill and cook until nearly done, about 6 to 7 minutes. Turn the flesh side down, cook for 1 minute, and remove to a platter. Dress the arugula with 4 tablespoons of the scented oil and some coarse salt and pile in center of platter. Serve warm or room temperature, with the remaining oil and lemon wedges on side.
All recipes copyright 2000, Mario Batali. All Rights Reserved.