lethargy is not really part of the adrenal fatigue picture, it's more like burnout. lethargic people (kapha) do better with a kick in the ass and exercising. adrenal burnout people get much worse from overdoing exercise.
so the general answer would be vata, but you have to always keep the person's constitution in mind. best to see a qualified vedic doctor to get your vikruti and prakruti down. it took me a bunch of tries to get that figured out, not so simple a thing even for the experienced doctors.