Preheat the oven to 325ºF.

Make the artichokes: Select a nonreactive bowl large enough to hold all the artichokes once they are trimmed and pour the 1/3 cup lemon juice into it. Working with 1 artichoke at a time, bend the tough outer leaves backward until they break at the point where the tough leaf becomes part of the tender base; stop when you reach the more tender interior leaves that are at least half yellow-green. With a serrated knife, cut across the leaves at the point where the color changes from yellow-green to dark green. Trim the stem of its outer layer, then trim the base, removing any dark green bits. Quarter the artichokes lengthwise and scoop out the hairy choke. As the artichokes are trimmed, drop them into the bowl holding the lemon juice and turn to coat. Toss occasionally to keep them coated with lemon.

When all the artichokes are trimmed, transfer them and the lemon juice to a large skillet along with the olive oil, garlic, thyme, bay leaf, salt, and pepper to taste. Bring to a boil over moderate heat, tossing to coat the artichokes with the seasonings, then transfer to the oven and cook until the artichokes are browned in spots and tender when pierced, about 35 minutes. Let cool, then cut each quarter into halves or thirds lengthwise.

In a bowl, combine the artichokes, onion, parsley, and olives. Just before serving, season to taste with lemon juice, using the 1/2 lemon.

Season the fish fillets on both sides with salt and pepper. Spread the coating or flour on a plate and dredge the fish on both sides, shaking off the excess.

Heat 2 skillets over high heat. Divide the olive oil evenly between the skillets. When hot, add the fish, reduce the heat to moderate, and cook until nicely browned, about 5 minutes. Turn the fish and cook on the second side until the fish is done throughout (test with a fork), about 4 minutes, depending on thickness.

Transfer the fish to a serving platter or individual plates. Top each portion with some of the artichoke salad. Garnish with the lemon wedges.