By Di Pasquale's recommendations if you work out in the morning then you may work out fasted if you prefer. The reason for doing this is that you may have more energy for working out since the body is not expending as much energy digesting all of the fat that you eat on this diet.
Someone in this thread suggested that they workout fasted on a CKD because of the depletion and fat loss benefits. This is a false statement as you will get the same depletion/fat loss benefits on a CKD or low carb variant such as the AD regardless of whether or not you eat pre workout (unless you are working out on a carb up day). It is when you ingest carbohydrates and begin releasing insulin preworkout that you can offset depletion and fat loss. For this reason, it also does not matter when you choose to do cardio during the day on this diet as you will achieve the same fat loss benefits regardless of whether or not you do it fasted.