One that's willing to test amino acids in a ME patient is a good one indeed. Some docs aren't good or understanding, but they don't mind ordering simple blood or urine tests.
I found this on a lab's site:
"Common indications for urine amino acid testing include clinical situations such as: 1) acute life-threatening episode, 2) failure to thrive, 3) recurrent vomiting, 4) neurological deterioration, 5) hyperammonemia, 6) lethargy, 7) metabolic acidosis, 8) testing or following therapy for a specific inborn error of metabolism (PKU, MSUD, tyrosinemia, etc.), and 9) kidney stones. Listing of clinical information is particularly important for appropriate interpretation."
If asking a doc I would be prepared with reasons. Point out that "lethargy" is a reason? Better if you had one of those other reasons like kidney stones would make it simple to convince the doc.