Place bacon in a large skillet and cook over medium-high heat, turning occasionally, until evenly browned, about 10 minutes. Drain bacon slices on paper towels; crumble.
Stir chicken, bacon, tomato, and celery together in a bowl.
Whisk mayonnaise, parsley, green onions, lemon juice, Worcestershire sauce, salt, and black pepper together in a bowl until dressing is smooth. Pour dressing over chicken mixture; toss to coat. Refrigerate until chilled, at least 30 minutes.
Stir chicken mixture and serve over romaine lettuce leaves; garnish with avocado slices.