But that was only true in the east; the lingua franca of the west was always Latin, not Greek. But even in the east, Latin was the language of government and law (including the imperial court in Constantinople) until Justinian. Hence the Corpus Iuris Civilis was promulgated in Constantinople in Latin, not Greek. The Strategekon of the Emperor Maurice in the late 6th cent. also indicates that commands in the army were still given in Latin
Greek was the lingua franca of the Eastern Roman Empire, which was the entire Roman Empire after the fifth century (the majority of the history of the Roman empire), which is why the Greeks associate themselves with the Roman Empire, which was my point. At the time of Christ, Latin was the official / native language of Romans, but Greek was more common in the empire as a whole. Hence, there were no Latin versions of the bible for a couple centuries.