Bring water to a boil in an 8-quart stockpot. Plunge lobsters headfirst into water. Return to a boil; cover, reduce heat, and simmer 12 minutes. Remove lobsters from water (do not drain); cool. Remove meat from cooked lobster tails and claws; cut into 1-inch pieces, reserving shells. Cover and refrigerate lobster meat.
Return reserved shells to water; bring to a boil. Reduce heat, and simmer 5 minutes. Drain through a colander over a large bowl, reserving broth; discard shells. Wipe pan dry with a paper towel.
Heat oil in pan over medium-high heat. Add onion, celery, carrot, and garlic; sauté 5 minutes. Add reserved broth, tomato, salt, saffron, thyme, pepper, and bay leaves; bring to a boil. Reduce heat, and simmer 15 minutes; discard bay leaves. Bring to a boil; add halibut, reduce heat, and simmer 4 minutes. Add clams; cook 1 minute. Add mussels; cook 2 minutes. Add shrimp; cook 3 minutes. Bring to a boil. Add reserved lobster meat; cook until thoroughly heated. Discard unopened shells.