For the Chicken: In a medium bowl, whisk together hot sauce and lemon juice. Add chicken and turn to coat evenly. Let stand at room temperature for 30 minutes.
Preheat oven to broil with rack 6 inches from heat source and line a rimmed baking sheet with aluminum foil. Remove chicken from marinade, letting any excess marinade drip back into the dish. Arrange chicken in an even layer on prepared baking sheet. Broil until a thermometer inserted into the thickest part of the thigh registers 170°F (77ºC), 10 to 12 minutes. Let rest 5 minutes. Slice chicken against the grain.
Meanwhile, for the Blue Cheese Dressing : In a medium bowl, whisk together blue cheese, mayonnaise, sour cream, buttermilk, vinegar, and salt. Season with pepper to taste, along with additional salt, if desired. Cover and refrigerate until ready to use.
For the Buffalo Dressing : In a medium bowl, whisk together hot sauce, oil, brown sugar, and lemon juice. Season with salt to taste. Cover and refrigerate until ready to use.
For the Salad : Using a vegetable peeler, peel carrots lengthwise to create long ribbons. Cover carrot ribbons with damp kitchen towel and set aside until ready to use.
In a large bowl, toss together romaine, cabbage, carrot ribbons, and ½ cup blue cheese dressing. Arrange on a large platter. Top with celery, tomatoes, cucumber, red onion, avocado, and sliced chicken. Drizzle with blue cheese dressing and Buffalo dressing, season with salt and pepper to taste. Serve.
