Place a wire rack on a baking sheet and put in oven- preheat oven to 200°
Cut lemon in half, juice 1/2 to make 2 Tablespoons liquid and thinly slice the other half. Set aside for sauce.
Place chicken pieces inside a resealable plastic bag with 1/2 tsp water added. Pound pieces with flat side of a meat mallet until 1/4-inch thick to form cutlets.
Dredge cutlets in 1/4 cup flour; shake off excess. Evenly coat cutlets in egg mixture, allowing excess to drip off. Dredge cutlets again in flour and shake off excess.
Heat 2 tsp oil in a large nonstick skillet over medium-high. Cook cutlets until golden on both sides, about 3 minutes each side, then transfer to prepared baking sheet in warm oven.
For the sauce, turn skillet down to medium, heat 1 1/2 tsp oil in same skillet add onion and cook until softened, 2-3 minutes. Add 1 1/2 tsp flour and cook 1 minute.
Whisk in broth, wine and lemon juice. Increase heat to medium-high and bring to a boil, whisking constantly. Reduce heat to medium and cook, whisking occasionally, until mixture reduces slightly and thickens.
Add butter to sauce; swirl to melt. Add half the parsley and season with 1/4 tsp salt and 1/4 teaspoon pepper; add lemon slices and coat with sauce. Serve cutlets with sauce and lemon slices; garnish with remaining parsley.