One thing about this period is that we have very few sources, and they get fewer after Justinian's death. You have to do some speculation to piece together what happened.
In Italy, I suspect that the various stories about how the Lombards arrived are just stories. Generally they reflect badly on the government at the time and I don't get the impression that the historical sources were friendly to to the government. What I suspect happened is that Lombard mercenaries were used to eliminate the Goths in Italy. The East Roman army at the time enrolled mercenaries and "barbarians" extensively, typical of later Roman armies. They were paid in land, again typical of the time given the absence of cash and shortage of hard currency. Once the Lombard mercenaries were used in Italy to remove the Goths, they just stayed, and slipped from imperial control. The fact that the Lombards were found throughout the peninsula, but did not control the ports or the Ravenna-Rome road is telling, that exactly fits where they would be if they were given land by the imperial government, away from the really important areas, but doesn't really match up well with what would happen after a contested invasion.
LIkewise imperial control tended to wane in the Balkans but there are no stories passed down about this.
If I am correct, what this implies that though the imperial government could and did destroy the Goths, keeping control of all of Italy was never on the cards. Probably the closest you could come was the resurrection of a new Western Roman Empire, with the Western Emperor incorporating the Lombards into his inner circle and keeping their allegiance.