Wash and dry chicken breasts. Pound to an even 1/4 inch thickness, and then place in a medium bowl and top with olive oil, lemon juice, and cajun seasoning. Cover the bowl with a lid, place in refrigerator, and marinate for 3-4 hours.
While chicken is marinating, peel and chop butternut squash. Place on parchment-lined baking sheet, drizzle with a tablespoon of cooking oil, sprinkle with salt and pepper, and roast at 450 degrees for 20-25 minutes until soft and beginning to caramelize.
While squash is roasting, wash and dry lettuce or spinach. Mix salad dressing ingredients in a jar or shaker container. Cook chicken in skillet in a tablespoon of olive oil over medium-low heat, for 3-4 minutes each side.
Place salad or lettuce in bowls, and then top with roasted squash cubes, nuts, cheese, and sliced chicken breasts. Serve immediately.