Make the broth: Fill a large 16–20 qt stockpot with water (about 12 quarts, leaving room for ingredients). Add Old Bay, Zatarain’s, lemons, onions, garlic, bay leaves, salt, and pepper. Bring to a boil.
Cook the potatoes: Add potatoes and boil for 20 minutes, until nearly tender.
Add corn + sausage: Stir in corn and sausage. Continue boiling for 10–12 minutes.
Remove vegetables: Lift out potatoes, corn, and sausage with a slotted spoon. Transfer to a large baking dish or sheet pan and keep warm.
Cook lobsters: Carefully add lobsters to the broth (in batches if needed). Cook 8–10 minutes, until shells are bright red. Remove and keep warm.
Add shrimp: Toss shrimp into the hot broth and cook 2–3 minutes until pink.
Assemble + serve: Scatter potatoes, corn, and sausage down the center of a butcher-paper-lined table. Layer lobsters on top, add shrimp, and serve with bowls of melted butter, hot sauce, and lemon wedges.