Sorry, what do you mean about "his brain shows he's not getting enough ", is it because of he's TSH? has he any symptoms? Did they checked calcium levels?
About the lactic acid, has he diabetes? Did they tested anion GAP , yes should go to a metabolic specialist, pediatric ENDO. He did the right thing about genetic tests (abnormalities of receptors of thyroid hormones), is any tests missing?.
I also wonder how the endo determined that your son's brain is not getting enough hormone.
Is he basing this on symptoms?
What are your son's lab results?
Was he born with hypothyroidism (congenital)?
Forgive me if this seems like prying, but how does the doctor know your son is over-medicated and yet his brain is not getting enough hormones?
Is your doctor experienced in pediatric endocrinology?
Just trying to get a feel for what is going on.