Place a large, heavy-bottomed pot over medium-low heat with the EVOO, about 4 turns of the pan. Add the anchovies, garlic and red pepper flakes. Cook a couple of minutes to melt the anchovies into the EVOO and toast the garlic slightly.
Add the onion, celery, thyme and bay leaf to the pot and cook for 3-4 minutes, until the veggies start to get tender. Season with salt and freshly ground black pepper, and add the wine or vermouth to the pot. Allow the liquid to reduce by half, then pour in the chicken and seafood stock, and bring up to a bubble.
While the pot is coming up to a bubble, season the scallops, swordfish, shrimp and calamari with salt and freshly ground black pepper. Add everything to the simmering pot, including the shellfish, and put a lid on it. Cook 5-6 minutes, until the clams and mussels open and everything is cooked through. During the last minute of cooking, stir in the calamari and allow it cook through.
Right before serving, stir in the parsley, lemon juice and zest. Serve the Cioppino straight out of the pot with plenty of crusty bread at the table to soak up the juices.