Its Volume VII in the “Barbarian Invasions of the Roman Empire” from the Folio Society, and the balance of power between the Byzantines, the Pope, and the Lombards is fatally broken by the fall of Ravenna to the Lombards. Now there is no Exarch to be the Pope’s political superior, even nominally.
Under a series of strong Popes at this time (720-760 AD) the Papacy realigned itself to find a new counterbalance to the Lombards – the Franks. Its king, Pippin, the father of Charlemagne, wasn’t hugely interested in intervening in Italy at first, but as a good Christian was influenced by the Pope’s cries for aid.
The point of contention was the Pope’s demand to get back part of the area around Ravenna. However, this time the towns would be under the rule of the Pope and not Constantinople. The King of the Lombards agreed under pressure, but then found reasons to delay turning over the cities. Pippin even defeated the Lombards in a few small wars but once the Franks returned home the king returned to his foot-dragging.
Then a new king, Charlemagne, took over the Franks. He soon had enough of the situation, and conquered the entire Lombard Kingdom and decided to rule it himself. Now the three-way split was the Pope, the Franks, and the Byzantines. And the Papacy was aligned firmly with the West and the Franks. But while the rift between East and West would continue to grow, the current happy relations between the Papacy and the Franks would not. However the breakdown would only happen outside the scope of these books.