Combine flour, 1 teaspoon salt, and pepper on a large plate. Put eggs on a separate plate. On a third plate, combine bread crumbs, zest from 1 lemon (2 teaspoon), 1 teaspoon salt, cheese, pine nuts, and basil. Sprinkle chicken with remaining 1/2 teaspoon salt. Coat both sides in flour, then eggs (allowing excess to drip off), then bread crumb mixture, pressing mixture in slightly.
In a large skillet over a medium flame, heat 1 tablespoon butter and 1 tablespoon olive oil. When pan is hot, add 1 to 2 chicken breasts; cook 2 to 3 minutes on each side, until golden and cooked through. Remove and keep warm on a plate tented with foil. Add more butter and oil to skillet with each batch. Cut remaining unpeeled lemon into large wedges. Squeeze 2 wedges over chicken before serving and place remaining wedges on platter with chicken.