Rome was ruled by the Ostrogothic Kingdom of Italy when Justinian took power, and hadn't had an Emperor since Julius Nepos/Romulus Augustus 50 years prior. Justinian attempted to retake Italy in the Gothic War, which was such a pyrrhic victory that it almost immediately fell to the Lombards. A few hundred years later Charlemagne conquered it again and it became Frankish. Basically aside from a brief period of time at the conclusion of the Gothic War, Rome was under Germanic rule from Odoacer onwards. And then the Middle Ages happened and it got very complicated.
There are a lot of definitions of "the Empire" and "when it fell".
For example, the fall of the Western Roman Empire is traditionally dated at 4 September 476, when Odoacer deposed Romulus Augustus. I think that was a Friday... bit hard to say as most perpetual calendars don't go back that far and of course it's an anachronism anyway :P
By the Fall of Constantinople, "the Roman Empire" was so in name only. That's why modern historians often use the term "Byzantine Empire".