T is low because LH is low.
We know that thyroid problems can be a primary cause of low T in some guys.
You cannot recover from your iodine deficiency with 150mcg [micro-grams] per day.
Your main focus should be your thyroid.
Were those body temperatures recorded when you first woke up and before you got out of bed?
Is your thyroid big? Neck looks thick there? Feels lumpy or asymmetric? Hi TSH over time can cause this. Low iodine over time can cause this.
I cannot easily interpret your T4 labs without ranges.
However: Thyroid function tests - Wikipedia
Suggests that fT4 mid range would be 13.5, so your 13.9 then appears good. If body temps are as you reported, they a good. This implies that your thyroid function is good but TSH is beating your thyroid to get there and there are serious risks of that. Please confirm body temps and timing.
This is standard advice maintained here:
There is a huge amount of knowledge in the stickies. Please study these. Start with the advice for new guys sticky.
There is a lot to read there, so read carefully. There are suggestions for things that are root causes of low testosterone [T]. Low T is a symptom, not a root cause itself. But low T itself is a root cause of many of the symptoms one experiences. Note that other things cause the same spectrum of symptoms, so do not have T tunnel vision. Many docs are guilty of that and they only treat the symptom [low T] and do not attempt to find the real problem. If you go to a clinic that specializes in low T, you will get T tunnel vision for sure.
Post info about yourself as suggested in the above sticky. We need labs, almost all of your labs, not just hormones. We also need the lab ranges.
We see a very high number of thyroid issues in the population of guys that show up here. So there is a strong focus on that. Most people are iodine deficient to some degree. Your history of iodine intake from iodized salt and vitamins that list iodine is important. If you become iodine deficient, the RDA [recommended daily allowance] is inadequate for recovery of iodine stores. Please see the thyroid basics sticky for more information.
You do not want to suffer from subclinical hypothyroidism or get Rx thyroid meds to treat iodine deficiency.
If you are injecting T or contemplating that, read the protocol for injections sticky.
There are stickies for finding a TRT doc, estradiol [E2] and lab work.
Do not place your history or treatment details in the stickies! That belongs in your thread. Keep all of your posts in your thread so we can have a clear picture of your situation and needs.