Heat grill or grill pan to medium-high. In a large bowl, whisk together the lemon juice, mustard, Worcestershire, Parmesan, 2 tablespoon oil and ¼ teaspoon each salt and pepper; set aside.
Brush the onion with 1 tablespoon oil and season with ¼ teaspoon each salt and pepper. Brush the bread with 2 teaspoon oil. Brush the chicken with the remaining teaspoon oil and season with ½ teaspoon each salt and pepper.
Grill the chicken and onion until the chicken is cooked through and the onions are tender, 5 to 6 minutes per side. Grill the bread until toasted and slightly charred, 1 to 2 minutes per side; rub each side of the bread with the garlic.
Slice the chicken and cut the bread into 1-inch pieces. Toss the romaine with the dressing. Fold in the chicken, onions and grilled croutons. Sprinkle with additional Parmesan, if desired.
