Not all studies say the same thing, it appears related to thyroid level, so 24 hours is close to the mark imo.
Liothyronine is readily absorbed after oral administration. About 5% of endogenous organic iodine in the blood is in the form of liothyronine and normal plasma concentrations are about 70ng/mL. Liothyronine is highly bound in plasma but to a lesser extent than thyroxine. It has a plasma half-life of about 35 to 60 hours. http://www.medsafe.govt.nz/Profs/Datasheet/t/Tertroxintab.htm