Yes liothyronine will cause hair loss, more so in women than men.
T3(liothyronine) stimulates several hormones ie; DHEA,IGF-1,Insulin,Estradiol,Testosterone (in higher doses can inhibit testosterone) and Progesterone.
DHEA,Testosterone and Progesterone can all have an end point of metabolizing to DHT, when DHT binds to the receptors in the scalp, we tend to lose hair, this becomes very individualized as some people are more prone than others (mainly men speaking) with females hair loss is sometimes caused by androgenic alopecia, same concept as male pattern baldness.
It's generally temporary with hair loss while supplementing T3, unless she keeps bumping her dose up which will stimulate more aforementioned.
The flip side is some topical shampoos will put a trace amount of progesterone in it as a topical DHT inhibitor at the scalp site. There's a slight difference in between oral and transdermal progesterone, oral progesterone has a higher degree to metabolise to Testosterone (keep in mind very minimal) to where transdermal is very, very minimal.
She could try REVITA Shampoo to see if that helps.