Bring water to a boil in a 12-quart stockpot. Add lobsters, cover, and cook 13 to 15 minutes. Set a colander in a large bowl. Working over colander, snip the tip of each lobster claw to release juices into bowl. Separate lobster meat from shells, and cut into bite-size pieces. Reserve meat and shells separately. Strain cooking liquid through a fine sieve lined with cheesecloth into bowl with lobster juices.
Using the same stockpot, melt 2 tablespoons butter over medium-high heat. Add chopped leek, corncobs, and reserved lobster shells. Cook, stirring, for 4 minutes. Add reserved lobster liquid, and simmer gently for 20 minutes. Strain through a cheesecloth-lined sieve. Discard solids.
Puree 1 cup lobster broth with 1 cup corn kernels. Melt remaining 1 tablespoon butter in a large pot over low heat. Add sliced leek, and cook for 2 minutes. Sprinkle in flour, and cook, stirring, for 1 minute. Stir in pureed corn mixture, and cook, stirring often, until broth thickens, about 2 minutes. Add remaining lobster broth, raise heat, and simmer. Add zucchini, summer squash, and remaining 2 cups corn, and cook until squashes are tender, about 2 minutes.
Stir in reserved lobster meat, and heat until warmed through, about 1 minute. Season with salt, and garnish with basil. Serve immediately.
Feel free to substitute three pounds of shell-on shrimp for the lobsters. Cook shrimp in step 1 until pink and cooked through, three to five minutes. Remove and reserve the shells, and continue with step 2.