Bring a large pot of water to a boil. Add the celery, onion, thyme, vinegar, and black pepper and boil for 10 minutes. Add the lobsters, cover, and simmer for 8 to 10 minutes, until shells are bright red and lobster is cooked through. Remove the lobsters from the water and immediately shock in ice water to stop the cooking. Shell the tail and the claws and cut the meat into 1/2-inch chunks. Reserve.
Cook the bacon until crisp. Drain on a paper towel lined plate and set aside.
Separate the egg whites from the yolks. Pass each separately through a medium strainer or food mill. Reserve.
Blanch the haricots verts in a small saucepan of salted boiling water for 1 minute. Drain and shock in ice water. Drain well and set aside.
Peel avocados, discard seeds, and cut into 1/2-inch chunks. Place in a bowl and cover with plastic wrap. Reserve.
In a mixing bowl, add the romaine and season with salt and pepper. Add 1/3 cup of the dressing and toss. Divide into 4 serving plates. Arrange the toppings in strips on top of the salad mix, starting on 1 end with the bacon, haricots verts, egg yolk, lobster, egg white, tomato, and avocado. Sprinkle the cheese all over the top. Serve the remaining dressing on the side.
Cobb Salad Dressing:
Combine shallot, Dijon, and vinegars in a large bowl and whisk well. While whisking, slowly drizzle in the oils until it is incorporated into the dressing. Season, to taste, with salt and pepper.