One of the previous threads is here
and the other one is here
If you had a low T4, that is a low level of thyroxine which is the main hormone actually produced by the thyroid, I would be expecting a fairly instant re check and treatment thereafter.
The recheck in 3 months route is usually taken if the levels of T4 and T3 are OK but the TSH, thyroid stimulating hormone, is a bit high. TSH does exactly what it says on the tin and is released by the pituitary gland which is a tiny gland just below the brain or out the back of the nose depending on whether you are an anatomist or a surgeon. Trouble is that the TSH will go up and down for all sorts of reasons particulalry other co-existent illnesses, viral infections etc. etc. hence the practice of repeating the test a few months later if the TSH alone is just a bit off.
If you do need replacement it is life long but in the vast majority of cases your body doesn't give a monkeys whether you get your thyroid hormone from Boots or make it yourself as long as the right amount is floating around. CG is right, there are some people where replacement is more difficult usually because of issues with absorption or in very rare cases because they don't process T4 to T3 as efficiently as they should. In my experience, it is a lot lot less than 15% of those affected and my job means I collect such people in a manner of speaking.
Thyroid advice on the internet is a perfect illustration of all that is good, bad and mad about the internet. The British Thyroid Foundation is a patient led registered charity that has a very informative website and strong connections with the British Thyroid Association which in turn serves the needs of boring people like me.