Combine the flour, oregano and parsley in a shallow dish. Season with salt and pepper.
Place a large skillet over medium-high heat. Dredge the fish in the flour mixture, shaking off the excess. Melt 3 tablespoons butter in the skillet, then add 2 fillets and cook until golden brown on the bottom, about 4 minutes. Flip and cook through, 1 to 2 more minutes. Transfer to a plate and keep warm. Repeat with the remaining 2 fillets.
Add the green beans and garlic to the skillet and cook about 2 minutes. Season with salt and pepper, then add the tomatoes and cook until just softened, about 1 more minute. Stir in the lemon juice and 1/4 cup water, then cover and cook until the beans are tender, about 3 more minutes. Remove from the heat and stir in the remaining 1 tablespoon butter until just melted.
Divide the fish and vegetables among plates. Garnish with oregano.