In that case, what would be some time periods in which the Lombards could reasonably take and hold Rome? Personally I think the earliest would be the early 7th century, and it would become easier the later the POD. The thing is, assuming we’re not butterflying Charlemagne, or the unification of France (is it too early to call them France?) under another ruler, I’m not sure they would have enough time to centralize even with Rome before they get conquered if our POD is in the 8th century. So here’s what I think this would mean in terms of the development of Italy in the Middle Ages. Take this with a grain of salt, because I am by no means an expert on this time period
If the POD is in the 7th century, I could see them managing to centralize and establish a hereditary monarchy. Given that they conquered Ravenna in 751 OTL, I could also see them conquering most, if not all, of Italy (though probably not Sicily). After Charlemagne, could that unification have carried over into the kingdom of Italy? Maybe italy splits off from the Carolingian Empire and is never part of the HRE, if such a thing exists ITTL. Medieval italy could be a very strong kingdom, at least in the north, not sure if they could hold the south.
If the POD is in the 8th century, medieval Italy is probably still the decentralized mess we saw OTL. Still, Rome might have more success exerting control over surrounding city states than it did OTL. Would the Pope still become the ruler of Rome ITTL? In both of these scenarios, I honestly have no clue what would happen to the Pope, or the development of the Catholic Church as a whole