Heat 2 tablespoons of oil in a medium saute pan over high heat until almost smoking and saute the tomatillos 3 minutes. Place the tomatillos in a food processor, add the parsley, basil, tarragon and water and puree.

Place the remaining 2 tablespoons of oil and the garlic in a medium saute pan over low heat and cook the garlic until cooked through. Raise the heat to medium, add the wine, and reduce the mixture to almost dry, 3 to 4 minutes. Add the clam juice and reduce by four-fifths.

Add the lemon juice and season to taste with salt and pepper. Add the butter and the tomatillo-herb puree, taste, and reseason if necessary. The salsa should be full flavored.

Combine the tomatoes, onion, parsley, red pepper flakes, vinegar, and oil in a mixing bowl and season to taste with salt and pepper.

Preheat oven to 350 degrees F. Kill the lobsters by inserting a sharp knife into the cross mark on the top shell between the heat and the body. Pull or cut off the claws. Pull or cut off the tails and cut in half lengthwise. Discard the bodies.

Heat the olive oil in a large ovenproof saute pan over medium-high heat until smoking. Season the lobster pieces to taste with salt and pepper and sear 3 minutes. Pour off excess oil. Add the salsa verde and potatoes to the pan and season to taste with salt and pepper. Place the pan in the oven and roast until the lobster is cooked through, 15 minutes. Reseason if necessary. Arrange the lobsters on a platter with the potatoes and sauce and spoon the relish over them.