For corn butter: Press the corn kernels through an electric juicer to extract the corn juice; discard the corn solids. Depending on the freshness of the corn, you should get at least 1 1/2 cups of corn juice. If you don’t have a juicer, blend the kernels in a high-powered blender, then transfer the mixture to a fine-meshed sieve and press the juices through the sieve and into a bowl.
Place the 1 1/2 cups of corn juice in a heavy, small, non-aluminum saucepan and whisk constantly over medium heat until the corn juice thickens into a pudding-like consistency and begins to bubble, about 10 minutes. (The natural starch in the corn causes the juices to thicken.)
Remove the pan from the heat and whisk in the thyme, then gradually add the butter, whisking to blend. Press a sheet of plastic wrap on the surface of the butter and set aside to cool to room temperature. Makes about 1 1/2 cups.
To prepare the lobsters: Bring a large pot of salted water to a boil over high heat. Once the water boils, add 1 lobster and immediately turn off the heat. Let the lobster cook gently in the hot water for 3 minutes. The lobster will be medium-rare at this point, which is what you want since they will be grilled later. Remove the lobster from the hot water and immediately place it in a large bowl of ice water to cool (a good ice bath consists of 75 percent ice and 25 percent water). Repeat with the remaining 5 lobsters, returning the water to a boil before placing each lobster in the water.
Preheat the barbecue for high heat, or preheat an indoor grill pan over high heat. Remove the claws from the lobsters. Using a very sharp large chef knife, cut the lobster bodies lengthwise in half and discard the intestines.
Oil the grill rack or grill pan. Brush the lobster tail meat generously with some of the corn butter. Grill the lobster halves, cut sides down, and all of the claws until grill marks appear on the meat, about 4 minutes. Turn over the lobster halves and claws and cook 2 minutes longer.
Transfer the lobster halves and claws to plates. Serve more corn butter alongside.