Cut apples into 1/8-inch matchsticks; toss with 2 Tbsp. lime juice. Peel and quarter avocados; toss with 1 Tbsp. lime juice.
Toss together romaine lettuce and next 2 ingredients; arrange on a large serving platter. Arrange tomatoes, next 4 ingredients, apples, and avocado over salad greens. Serve with Cider-Sorghum Vinaigrette.