Fill a large stockpot 3/4 full with salted water and bring to a boil. Plunge the lobsters headfirst into the boiling water and blanch for 7 minutes. Transfer tongs to a large bowl filled with ice water to cool. When the lobsters are cool enough to handle, crack the shells and remove the meat from the tail if using a spiny lobster, and from the tail and claws if using a Maine lobster. Cut into bite-sized pieces and set aside.

Melt 4 tablespoons of the butter in a small saucepan over medium heat. Add the flour and cook, stirring constantly with a heavy wooden spoon, to make a blond roux, 5 to 6 minutes. Remove from the heat and cool.

Combine the saffron threads, 3 tablespoons of the lemon juice, and the sherry in a small bowl and stir to blend. Set aside.

Heat the olive oil and remaining 1 tablespoon butter in a large, heavy stockpot or Dutch oven over medium-high heat. Add the onions, yellow bell peppers, red bell peppers, and poblano peppers, and cook, stirring until soft, about 4 minutes. Add the shallots and garlic and cook, stirring for 1 minute. Add the tomatoes, tomato paste, achiote powder, salt, and pepper, and cook over medium-low heat, stirring occasionally, for 15 minutes. Add the saffron mixture, stir, and bring to a boil. Add the shrimp stock and roux, and whisk to dissolve the roux. Bring to a boil and boil for 3 minutes. Reduce the heat to low and add the reserved lobster meat and simmer until just cooked through, about 3 minutes.

To serve, ladle about 1 cup of stew into each of 6 large soup bowls. Garnish each with about 2 tablespoons of the olive salad, 1 tablespoon of basil, and 1 teaspoon of extra-virgin olive oil.