Combine the fennel seed, peppercorns, coriander seed, red pepper flakes, and bay leaves and tie in a cheesecloth bag. Put the bag in a large pot with the water, the lemon halves, the garlic, the wine, and the salt. Cover and bring to a simmer, then simmer for 10 minutes.
Add the potatoes, onions and artichokes and simmer gently, covered, until they are tender. As they are done, remove them to a serving platter. The potatoes may take 20 minutes or more; the onions and artichokes will take 30 to 40 minutes.
After you have removed all the vegetables, add the lobsters. Cook just until they turn pink, about 15 minutes. Remove them with a slotted spoon to the serving platter. Then add the shrimp and clams and cook until the shrimp turn pink and begin to curl and the clams open fully, about 5 minutes.
Cut the onions in half. Cut the artichokes in half and scoop out and discard the chokes.
Serve the shrimp, potatoes, onions, and artichokes with shallow bowls of melted butter, sea salt and the Fennel Spice Rub for dipping, and with jars of hot sauce.