A more likely option I can see is that some foreign people different to Franks wipe the Lombards out of Italy and restore the HRE in an analogue way to Charlemagne's, but keeping the center of the Empire actually in Rome/Milan/Ravenna. Maybe the Avars or the Magyars could be an option if they would have been 'Romanized' quickly by some way.
I don't feel that that's particularly likely. Most Italians didn't have much problem with the Lombards, but one important one did: the Pope. The Popc throughout the Lombard period was terrified by being surrounded by a united Lombard state and made subservient to it, and resorted to playing different powers against one another to prevent this from happening (the Lombard King, different powerful factions, the Byzantines, the Franks as well as the two southern Lombard Duchies of Benevento and Spoleto). Its interesting to note that this did not change after the Lombards converted to Catholicism.
That being said, there is no reason to assume that a Lombard King couldn't unite the entire peninsula - this actually came very close to happening under King Luitprand. However, in order to do so, they are going to have to deal with the Pope; either finding some accord (such as setting the Duchy of Rome aside and promising to recognize the Pope's authority there in exchange for something. Though this was tried a number of times with the Pope often refusing) or else marching on the city and replacing the Pope with a more compliant pontiff.
However, I can't see any other group invading Italy to be more successful than the Lombards, as the Pope would still be worried about being encircled and losing his independence.