1. Place chicken breast halves in a large resealable plastic bag with lemon juice, olive oil, and lemon pepper. Shake to coat, and marinate in the refrigerator for at least 1 hour.
2. Preheat a grill for high heat.
3. Lightly oil the grill grate. Place the Vidalia onions and mushrooms on the grill, and cook until lightly charred on both sides; set aside. Place chicken onto the grill, and discard marinade. Cook for 15 minutes, turning once, or until juices run clear. Remove from heat, cool, and chop.
4. In a large bowl, thoroughly mix the onions, mushrooms, chicken, and mayonnaise. Season with hot sauce, salt, and pepper. Cover, and refrigerate until serving.