1. Bring 1 1/2 cups water and 3 tablespoons juice to a boil in a Dutch oven. Add mussels; cover and cook for 2 minutes or until shells open. Remove mussels from pan with a slotted spoon; discard any unopened shells. Cool. Remove meat from the mussels; discard shells. Place mussels in a large bowl.
2. Add shrimp to boiling liquid in pan; cook 2 minutes or until done. Remove shrimp from pan with a slotted spoon, and add to mussels. Cut squid crosswise into 1/4-inch rings, and leave tentacles whole. Add squid to boiling liquid in pan; cook for 1 minute. Remove the squid from pan with a slotted spoon. Cool; add squid to mussels mixture. Add lobster to pan, and cover, reduce heat, and simmer for 8 minutes. Remove lobster from pan, reserving 1 tablespoon cooking liquid; cool lobster. Remove meat from lobster tail and claws; coarsely chop. Add lobster, salt, and black pepper to mussels mixture.
3. Combine the remaining 3 tablespoons juice, reserved cooking liquid, and olive oil in a bowl, stirring with a whisk. Drizzle lemon mixture over seafood mixture; toss gently to coat. Cover and marinate in refrigerator for 1 1/2 hours. Add cilantro and remaining ingredients to seafood mixture, and toss gently.
Sustainable Choice: What About Gulf Shrimp? According to Monterey Bay Aquarium Seafood Watch, Gulf shrimp are considered a good alternative. Post oil spill, the U.S. government says they've tested safe to eat.