Begin by preparing the turkey. Pat it dry with paper towels, ensuring the cavity is also dry.
In a small bowl, mix together the Cajun seasoning, garlic powder, onion powder, paprika, black pepper, cayenne pepper, and salt.
Rub the seasoning mixture all over the turkey, including under the skin and inside the cavity. Squeeze the lemon halves over the turkey and place them inside the cavity along with the onion, garlic, and thyme.
Allow the turkey to marinate for at least 2 hours, or preferably overnight in the refrigerator for deeper flavor.
When ready to fry, set up your deep fryer or a large, heavy-duty pot outdoors (ensure it's on a flat surface away from flammable materials). Fill it with peanut oil, leaving enough space for the turkey to be submerged without overflowing.
Heat the oil to 350°F. Use a thermometer to monitor the temperature.
Carefully lower the turkey into the hot oil using a turkey fryer basket or a sturdy hook. Fry for about 3 to 4 minutes per pound. For a 12-pound turkey, this will take approximately 36 to 48 minutes.
Once the turkey reaches an internal temperature of 165°F in the thickest part of the breast, carefully remove it from the oil and let it drain on a wire rack or paper towels.
Allow the turkey to rest for at least 20 minutes before carving to let the juices redistribute.