Preheat a grill to medium-high heat.
In a bowl, add the mayonnaise, Worcestershire, lemon juice, mustard, vinegar and garlic and whisk until combined. Slowly whisk in the olive oil. Add the Parmesan and continue to whisk. Season the dressing with salt and pepper.
Drizzle olive oil on the romaine hearts and season with salt and pepper. Place the romaine cut-side down on the grill and cook until nicely marked, 2 to 3 minutes. Brush the bread slices with olive oil and place on the grill. Cook until grill marks appear on both sides and the bread is crispy, about 5 minutes.
Spread the sugar out on a small plate. Dip the cut sides of the lemons into the sugar. Place the lemon halves on the grill and cook until slightly charred and grill marked, 2 to 3 minutes.
Cut the bread into bite-sized pieces. Place the romaine hearts, croutons and lemons on a wooden board and serve with the Caesar dressing.