In a large covered kettle, bring 6 quarts salted water to a rolling boil over high heat. Add the lobsters, cover, and cook for 10 minutes. Drain and cool under cold running water. With poultry shears, cut away the claw and tail shells and carefully remove the meat. If the lobsters are female, reserve the grainy red coral and chop finely. Cover and refrigerate the lobster meat and coral.

With a sharp knife, cut the kernels off the cob, slicing from the top of the ear downward, but not too close to the cob. You should have about 4 cups. Using a small spoon, scrape the milky liquid from the cobs into a medium bowl. Add the kernels and reserve.

In a medium saucepan of lightly salted boiling water, blanch the lima beans until almost tender, 3 to 5 minutes. Cool under cold running water. Drain and reserve.

In a large heavy nonreactive saucepan, melt the butter over medium heat. Add the cream. When it begins to steam, add the corn and its pulp and cook for 10 minutes, stirring often until the liquid thickens slightly. Add the lima beans and cook another 2 minutes until the beans are just tender. Add the lobster meat and cook an additional 3 minutes until the meat is warmed through. Season with the cloves, cayenne, salt, and pepper. Fold in the chives.

Spoon the succotash and lobster in equal proportions into 4 warm soup plates and serve.