[kabumpo]

Justinian was in Byzantium, the eastern part of the empire that lasted longer.

[Verginius Rufus]

Justinian was from near Skopje in the present-day Republic of Macedonia--one of the last emperors who spoke Latin as his first tongue (although my guess is that Cicero would have cringed at what passed for Latin in the rural Balkans in the sixth century). The future pope Gregory the Great spent some time in Constantinople a little later and somehow managed not to learn Greek, so there must have been a critical mass of Latin-speakers even in Constantinople.

In the second half of the sixth century or first part of the seventh century much of the Balkans was overrun with Slavs (including some parts of Greece which were later re-hellenized). Although much of the territory was again under the control of Constantinople from time to time, that must have tipped the scales heavily in favor of the Greek language as opposed to Latin. Justinian's law code was in Latin but already a lot of the new laws were being issued in Greek.