Q: Could the capital of the Roman/Byzantine Empire return to Rome after Justinian if there is no Langobardic invasion of Italy?

[JanWellem]

After the 6th century Gothic War had trashed central Italy Rome had pretty much become a late antique version of Detroit, being only a shadow of its' former glory days' grandeur.

 

[Silver01]

In fact, Constantinople was far more exposed to external attacks (Persians, Avars, Bulgars, Arabs and finally Turks)

the comparison here makes no sense you lumped in about 500 years of history
by that logic i can say italy from 650 to 1100 was attacked by franks , then hugarians , the HRE numerous times arabs and normans.

- The Franks would have been probably not interested in attacking Italy without Papal consent, and by the 8th-9th century they would be mostly the only great power able to disturb Italy, because probably the Arab expansion would have been not that aggresive with a stronger Byzantium ITTL. As long as the relations between the Franks and the Pope do not strain, it is unlikely they would intervene in Italy.

the franks attacked italy as early some at the request of the romans some even after the arab invasions example constans went to attack benevento because the lombard king was busy dealing with frankish invasion that the pope nor constans asked for.

also a stonger byzantine empire means that they have no reason to flee west .