Well, there is some speculation that one of the Germanic dialects present in modern day Italy is actually a descendant of Lombardic. I'm not sure if this is true (I'm not linguist, as I always stress), but if it is, then some form of the Lombard tongue survived to the present day.
I actually think that Lombard becoming the dominant language in northern Italy is doable if we sent the point of divergence back far enough. I think a lot of modern readers forget just how depopulated Italy was after the Gothic wars, and when ever there is that much of a population vacuum, its at least possible for a new language to become entrenched. Personally, I think one of the things that would help is if the Reign of the Dukes never happened. Make sure that Albion and Cleph are not assassinated, and maintain a strongish monarchy from the earliest days forward. With each Duke not going off on his own, you might actually see a slower conquest of southern Italy as well as an even more concentrated Lombard settlement in the north. Also, it would help if these Kings could continue to invite Saxon and Bavarian allies in to help settle the country (if they feel a bit threatened by the power of their own Dukes, they may do this to introduce a population that will be loyal to the themselves.). This would further entrench the Germanic identity of the region.
Next, it is important to keep the Lombards Arian. This shouldn't be entirely impossible, due to the long standing rivalry between the Lombard kings and the Pope. As long as the Lombards remain Arian they can not assimilate completely into the local culture and will always be differentiated.
Latin is always going to be a language of prestige and government, and I don't think there is anyway to counteract that at this point in history. However, if modern day Lombardy is settled by enough Lombardic and Germanic speakers, you may well see the everyday people of that region begin to adopt the language simply to get by in life (they would need it to trade, conduct business, and communicate with their neighbors). In that case, Lombardic would become entrenched and could grow to become the dominate language of the region. This, of course, is only in the North; I don't see any conceivable way to make Southern Italy speak Lombardic.