I am already hypothyroid (Hashimoto's), and I've read all the nonsense about how low carb/low calorie, etc. will 'ruin' the thyroid.
But I was massively overweight and needed to eat both low carb and low calorie to lose the close to 200 lbs that I've lost over the past few years. My endo was delighted with my WOE, and when I mentioned some of the things I'd read on the Internet about how my low level of carbs/calories would 'damage' my thyroid, he said that was not true. I eat very low carb because I'm extremely carb sensitive.
My endo tests my hormone levels every 4 months, and there have been no changes based on my WOE. However, one item in Peter's blog interested me. Most of the internet 'experts' claim that the T3 'must' be at the upper levels of the lab range to be normal. Peter suggests that it's possible that someone eating low carb would thrive at a lower level of T3 (and the TSH would confirm that). My T3 is rarely higher than half of the lab range--when I feel fine, have no symptoms, and my TSH is in a good place.