Bring a medium pot of water to a boil, add the asparagus and cook until tender yet firm, about 2 to 3 minutes. Drain and run under cold water to stop it from cooking further. Set aside.
In a small bowl combine the oil, lemon juice, salt and pepper.
In a large bowl combine the asparagus, lobster, tomatoes, red onion, basil and dressing. Divide equally in 2 bowls and eat right away.