For the salad, combine the cooked chicken and BBQ sauce in a medium bowl. Refrigerate until ready to use.
In a large bowl, toss together the iceberg lettuce, romaine lettuce, red onion, cilantro, corn, black beans and cheese. Toss the mixed salad with about 1/4 to 1/2 cup of the dressing, if desired. Otherwise, you can serve the dressing on the side. Place salad on plates and top with the prepared BBQ chicken and additional dressing.
For the dressing, combine all the ingredients together and whisk (or shake, if using a jar) vigorously to combine. You could also run this through a blender to make it even more smooth. Refrigerate until ready to serve.