Whisk together first 9 ingredients in a medium bowl, whisking until smooth; add salt and pepper to taste.
Coat cold grill grate with cooking spray. Preheat grill to 350° to 400° (medium-high) heat. Lightly coat cut sides of avocados and lettuce with cooking spray; season with salt and pepper. Grill avocado halves and lettuce, cut sides down and covered with grill lid, 1 minute or until grill marks appear.
Slice avocados. Chop lettuce, and arrange on a platter. Top with avocado, radishes, and blue cheese. Drizzle with dressing. Add salt and pepper to taste.