Cook onion in butter in a large skillet over medium-high heat, stirring constantly, until tender. Add giblets and wine. Bring to a boil; cover, reduce heat, and simmer 45 minutes or until giblets are tender.
Add lemon, and cook, uncovered, 2 minutes. Place bread cubes in a large bowl.
Pour giblet mixture over bread cubes; add Parmesan cheese and remaining ingredients, tossing mixture well.