Bring a pot of salted water to a boil. Add the lemon halves and garlic, then submerge a large heatproof strainer in the water. Soak the red onion in ice water while you cook the seafood. Fill a large bowl with ice water; set aside.
Add the shrimp to the strainer in the boiling water and cook until pink, about 2 minutes; carefully remove the strainer and add the shrimp to the large bowl of ice water. Bring the water back to a boil, return the strainer to the pot, then add the scallops and simmer until cooked through, about 2 minutes; remove the strainer and add the scallops to the ice water. Repeat with the calamari, cooking until they just turn opaque, about 2 minutes. Repeat with the mussels, covering the pot; cook until the shells open, about 5 minutes. Drain the seafood from the ice water and remove the mussels from their shells; pat the seafood dry.
Drain the red onion and pat dry. Combine the seafood, red onion, celery, fennel, olives and parsley in a large bowl. Drizzle with the lemon juice and olive oil and toss; season with salt and pepper. Let stand 30 minutes before serving (or refrigerate up to 4 hours; bring to room temperature before serving). Top with fennel fronds. Photograph by Con Poulos