Apes- My thyroid was Overactive but I do know a bit about underactive aswell because a few friends have theirs under. The poor thing feeling ran down and tired etc- even when your thyroids over you can feel that way..never losing weight is very common (For overactive you can lose drastic amounts of weight & I was one of those rare cases i australia who PUT alot of weight on!)..The meds DEFINATLY help and your sisters probably done the right thing by getting it checked earlier whcih means with the meds her levels should be able to go to normal pretty quickly. I didn't take any when I was pregnant at first but I ended up under the care of an Endocrinologist (Is your sister pregs? if so-Get her GP or ObGyn to refer her to one who can watch her throughout the pregnancy, they keep levels in check). The Endos were great-they kept my levels in check & put me back on meds when I was about 25weeks pregnant. As far as I know Thyroid meds are safe to take from second trimester-but don't quote me on that because it will all depend on what medication she will end up taking etc..
Hopefully once your sister starts taking the medication she will start feeling less tired & gain more motivation..I always know when my thyroid is out because I get tried & really puffed (I get puffed coming back from the letterbox)! Feel free to ask me anything..I do have a thyroid support group I started in another Mothers forum where there are a few with Underactive thyroids- your sister (or you) are more than welcome to pop on there and ask anything aswell (Or you can catch me here-or FB)