Heat the olive oil in a large skillet over medium heat. Add the anchovies, bay leaf and red pepper flakes and cook until the anchovies begin to dissolve, about 2 minutes. Add the garlic, onions and some salt and pepper. Saute until the onions are translucent, 8 to 10 minutes. Stir in the tomatoes and parsley and use a wooden spoon to crush the tomatoes into bite-size pieces. Reduce the heat and simmer for 10 to 15 minutes to blend the flavors.
Season the fish fillets and scallops with salt and pepper. Raise the heat under the skillet to medium. Add the mussels and clams and gently stir to combine. Cover and cook 4 to 5 minutes. Add the fish, shrimp and scallops and gently stir to combine. Cover and cook until the seafood is cooked and the shellfish are open, an additional 4 to 5 minutes. Stir in the lemon juice and serve immediately.