How to Make It
In a large saucepan of boiling salted water, cook the potatoes until tender, about 20 minutes. Drain and let cool completely. Cut into 1/2-inch dice.
Bring a large pot of salted water to a boil. Add the lobsters, head first, cover and return the water to a boil. Uncover and boil the lobsters over high heat until the shells are bright red, 8 to 10 minutes. Using tongs, transfer the lobsters to a large bowl of ice water to cool; drain. Twist off the claws and tail and remove the meat. Add the claw meat to a large bowl. Remove the intestinal vein that runs the length of the tail. Cut the tail meat into 1/2-inch dice and add to the bowl with the claw meat.
In a medium saucepan of boiling salted water, cook the corn until crisp-tender, about 1 minute. Drain and refresh under cold water. Drain again and pat dry. Add the corn, diced potatoes, crème fraîche, mayonnaise and lemon juice to the lobsters, season with salt and pepper and mix well.
Arrange the sliced tomatoes on one side of 8 plates or a large platter and season with salt and pepper. Spoon the lobster salad next to the tomatoes, garnish with the chives and serve.