So, somehow, a post about the Lombards has already been sidetracked into speaking about Charlesmagne and the Saxons!?
In my opinion, the biggest problem that the Lombards had to deal with was the Pope and, even more importantly, the Byzantine territory of the Exarxh of Ravenna. By effectively dividing their territory in half, it made it very difficult for the Kings to consolidate his influence over the southern Dukes of Spoleto and Benevento.
What you had in Italy at the time was a situation where the Lombards had to continually manuever around the Byznatines and the Pope. When they were finally able to knock one of them out, such as when Desiderius took Ravenna, the Pope would just call in the Franks who were more than happy to come marching down and cause some havok.
If you want to see a strong Lombard state in Italy, what you are going to have to do is fracture Frankish power in the north for a generation or so. Maybe given Charlemagne two more brothers, so the kingdom is split into four, or some such. Anything that works. But, without the Franks there to destabilize Italy, the Lombards might just have a chance to unite the peninsula.
Of course, if the Kings do that, they will have to deal with their own nobility which had a long standing tradition of disliking strong royalty (The Lombards actually went without a King for about 10 years, after entering Italy), as well as the afore mentioned semi-independent dukes of benevento and Spoleto. But, The Lombards were not the only peoples of the time who had to deal with such a situation, so they might well have been able to pull through. That is, as I said, if the Franks are unable to intervene.
On an interesting note, a surviving Lombardy is going to have to influence upon the temporal powers of the Pope. It was during this time that the Pope began to see himself as the ruler of, not jsut the city of Rome, but the territory outside as well. This claim was backed up, and made stronger, by charlesmagne and the creation of the Papal States. This is unlikely to occure in *Lombard Italy.