Rinse Walleye and pat dry with paper towels.
In a shallow bowl, whisk together the flour, Herbs de Provence, salt, and pepper. Dredge the fish in the flour, tapping off excess flour. If the walleye filets are thick, slice them lengthwise so they are thin, like a Dover Sole filet.
Heat the olive oil and butter in a cast iron skillet over medium heat. When hot but not burning, add the fish. Make sure each piece is not touching another. If needed, do multiple batches. Cook until the fish is golden brown, then flip and cook until that side is golden brown. Transfer the fish to a platter and repeat until all the fillets are cooked. Lower the heat to medium-low, and add the lemon juice, capers, and caper juice to the pan. As soon as the sauce bubbles, whisk in one tablespoon of butter and remove from heat. Pour the sauce over the fish and garnish with parsley. Serve immediately.
Note: This dish is terrific to serve with green beans, roasted potatoes, air-fried potatoes, mashed potatoes, etc.