In a food processor or blender combine oil, lemon juice, parsley, and garlic; cover and process until finely chopped. Add salt and pepper to taste.
Transfer parsley mixture to a large skillet; add meatballs and heat through, covered, over medium heat, stirring and spooning sauce over meatballs occasionally.
Place one ciabatta roll, toasted side up, on each plate. Top with shredded romaine. Remove meatballs from skillet with a slotted spoon; place atop romaine. Drizzle warm parsley mixture over meatballs. Makes 6 servings.