Set a large 6-gallon stockpot to boil over high heat. Once the water comes to a boil, immerse the lobsters in the pot. Cook the lobsters for 3 minutes, remove, and chill immediately in an ice bath. Once the lobsters are cool enough to handle, remove from the water and place on a kitchen towel draped over a cutting board.

Twist the tails off the lobsters, and cut the tails in half lengthwise using a large chef's knife (score along the length of the tail). Set the cut tails aside, and crack the shells of the claws to remove the meat. Reserve the claw meat for pasta or a salad for a later date.

In a small saucepan over low heat, add the salt and pepper, lemon zest, lemon juice, tarragon and butter.

To finish the dish, set the grill on medium-high. Brush the lobster tails with the olive oil on the cut end, and season with salt and pepper. Place the tails, cut side down on the grill, and cook for 3 minutes, rotate 45 degrees, and cook for an additional 3 minutes. Turn the lobsters over and cook for 2 minutes. Once tails are cooked through, brush with lemon tarragon butter.

Using a large saute pan, heat the olive oil over medium-high heat, add the sliced okra. Cook the okra for 5 to 6 minutes until golden brown, tender and no longer slimy. Add the corn, lima beans, tomatoes, butter, and parsley and cook, tossing gently, until the vegetables are just tender, 3 to 4 minutes. Fold in avocado. Season with salt and pepper, to taste.

Preheat grill on high heat. Peel the sweet potatoes and slice crosswise into 1/3-inch slices. Lightly brush the slices with olive oil and place onto the hot grill. Cook for 5 to 7 minutes on each side, or until nicely marked by the grill and tender.

To compile the dish, divide the sweet potatoes between 4 dinner plates. Top with succotash and place 1 whole lobster tail (or 2 halves) on each plate.