Gently toss tomatoes, oil, vinegar, sugar and garlic together. Place them cut side up on a large rimmed baking sheet. Season with salt and pepper. Bake for 25-30 minutes until the tomatoes begin to caramelize . Remove from the oven and set aside to cool.
Divide the lettuce onto serving plates. Top with tomatoes, lobster, bacon, hard boiled eggs, avocado slices, green onions, and blue cheese. Drizzle dressing over salad and serve immediately.