Peel and wash the broth vegetables: celery, carrot, onion and bay leaf. Fill a large pot with water and bring to a boil with the vegetables, add a handful of salt and then add the previously washed lobster.
Cook for 20 minutes. Meanwhile, prepare the salad. Thinly slice the celery and fennel; peel the grapefruit and carefully cut out the pulp leaving any white skins out. Cut into cubes.
Arrange everything in a bowl, add the olives and season with oil, lemon juice, salt and pepper. Drain the lobster, remove the vegetables. With the help of scissors cut open the back of the lobster. Peel the tail and cut the flesh into thick medallions, around an inch thick.
Arrange on a plate, over the seasoned salad. Finally, sprinkle with the chopped parsley.