Put 4 tbsp. lemon juice and 6 cups water into a large bowl. Working with one artichoke at a time, place an artichoke on its side. Using a serrated knife, cut the leaves crosswise about 1 1⁄2" from the point where the leaves meet the base; discard leaves. Cut away the tougher, dark green leaves until you reach the inner yellow leaves. Using a peeler, remove the green outer layer of the stem and base. Cut off the bottom 1⁄2" of the stem and trim away any remaining green parts from the underside of the base. Scoop out fuzzy choke at the center of the artichoke. Quarter artichoke and transfer it to the bowl of lemon water. Repeat.
Drain artichokes. Heat oil in a 12" skillet over medium-high heat; add garlic, onions, and scallions and cook, stirring occasionally, until soft, 3 minutes. Add artichokes and 2 cups water. Bring to a boil, reduce heat to medium-low, and cook, stirring occasionally, until artichokes are tender, about 25 minutes. Add fava beans and cook, stirring occasionally, until tender, about 5 minutes. In a small bowl, stir together remaining lemon juice, flour, and 1 tbsp. cooking liquid; add mixture to skillet and cook until liquid is slightly thickened, about 3 minutes. Stir in half the dill; transfer to a serving bowl. Serve hot or at room temperature, garnished with the remaining dill.