Preheat the oven to 425 degrees F. Cut the potatoes, without peeling, into thick slices and each slice into quarters. Put them into a large roasting pan with the whole garlic cloves.
Quarter the onions, peel them (I find it easier to do it this way around), then halve each quarter horizontally. Quarter the lemon and cut each quarter into 1/2-inch pieces. Add the onion and lemon to the pan with the potatoes and garlic.
Drizzle with 2 tablespoons of the oil and roast for 1 hour.
Meanwhile, soak the clams in a bowl of water - if any are smashed or don't close after they've soaked, throw them away. Slice the squid into rings.
After 1 hour, take the pan out of the oven and put it over low heat on the stove top so that the pan doesn't cool while you add the seafood.
Arrange the drained closed clams, baby squid rings, and whole raw shrimp over the potatoes, garlic, lemon pieces, and onions.
Splash the seafood with the remaining 2 tablespoons of oil and the vermouth, then season with salt and pepper, to taste.
Put the roasting pan back in the oven for 15 minutes, by which time the clams should have opened and the shrimp have turned pink. Discard any clams that have not opened.
Scatter with parsley and serve straight from the pan: it couldn't look more beautiful.
Make Ahead Note: Potatoes can be prepared 1 day ahead. Submerge in a bowl of water and store in the refrigerator. Drain and pat dry before using. Onions and lemons can be cut 1 day ahead and stored in bowls tightly covered with plastic wrap in the refrigerator.