Bring a large pot of unsalted water to a boil over high heat. Add the corn and cook for 3 minutes. With tongs, remove the ears of corn from the pot and set them aside to cool. Salt the water generously (it should taste like the sea) and return the pot to a boil. Add the lobsters and cook uncovered for about 8 minutes. Check for doneness by twisting the tail off one lobster. The meat should be opaque throughout. If it's still translucent, continue cooking for another minute or two. Drain and let cool. Crack the shells; remove the meat from the tails and claws. Slice into 1/2-inch pieces and refrigerate in a bowl until ready to use.
In a medium bowl, combine the lemon juice and vinegar with 1/2 tsp. salt and a few grinds pepper. Whisk in the olive oil in a thin stream. Slice the corn kernels off the cobs. Add the kernels to the vinaigrette, along with the tomatoes, jalapeños, shallots, and basil. Toss gently, taste, and adjust the seasonings if needed. Put the greens in another bowl.
Tilt the bowl with the tomatoes and spoon off about 4 Tbs. of the juices. Add this to the bowl of greens and toss to coat. Spoon off about 3 more Tbs. of juice from the tomatoes and add this to the lobster; toss to coat. Taste both the greens and the lobster; adjust the seasonings as needed.
Divide the tomato salad, lobster, and greens evenly among four plates, arranging them in separate mounds, and serve.