TheLohoped
Known today as TLPD-AVW
No, it wasn't. at least during Justinian-Theodora era. greek became offical language of Byzantine Empire after 620. and if you want to know, Theodora lived in 6th century (500-548) and in her era Latin was offical language of Byzantine Empire.
Latin was the official language of the empire but the majority of population spoke greek. Only the high class officials spoke latin. Since Theodora was from the low class before marrying Justinian (very low class) it's logical that she speaks greek and not latin.