Especially if you goal is to lose fat, I would start taking a low dose of T4. I'd start at 50mcg and see how you feel. You can take more, but I would start there. If you are feeling good at 50mcg, go back in and get tested, to see where you're at. Taking GH will increase the conversion of t4 to t3, leaving t4 low but I wouldn't be surprised if t3 levels are higher because of the increased turn over. Feeling tired and lethargic could easily be hypothyroid due to low t4. I imagine that t4 will increase your energy levels and I would expect to start to notice a difference within a few days.