Preheat grill to medium (300F to 350F). In a medium bowl combine tomatoes, corn and basil. Set aside.
Place lobsters belly-side down. Insert the tip of a large knife at the cross mark right behind the head and cut through the head, cut it in half lengthwise from head to tail. Scoop out the roe and tomalley (reserve, if desired).
Pull the claws and legs from lobster. Crack claws lightly with mallet. Place on grill; grill 5 to 7 minutes per side.
Brush lobster meat with oil and season with salt and pepper to taste. Grill lobster, shell side down, 5 minutes. Turn and grill 3 minutes more. Remove and let cool.
Meanwhile, for dressing, in a small bowl whisk together vinegar and mustard. Slowly whisk in oil until well-combined. Season with salt and pepper to taste. Set aside.
When the lobster is cool enough to handle, remove meat from shell. Coarsely dice meat and add to bowl with tomatoes and corn. Add dressing; toss to coat. Place lettuce leaves on the plate. Spoon lobster salad on lettuce and serve.