So I'm going to begin with the simple (but inexact) answer, and then proceed to the harder (but more accurate) answer.

The simple answer (which isn't even that simple) is, estimations of the Lombard migration into Italy around 568 CE max out at around 200,000 presuming a super low Italian population of 2 million, thus making the maximum percentage about 10%.

The longer answer (which isn't even that accurate) is the percentage is likely much lower at the point of migration. The percentage of the population 200,000 would be for Italy varies depending upon your estimates of Italian population are at this time, keeping in mind it's coming off the backs of not only the Justinian Plague, but also the 30 year long Gothic War and its associated famine and socio-economic breakdown. Best guesses are between 2 million and 5 million (keep in mind the population of the Roman Empire as a whole at its peak are around 50 million). However even the 200,000 for the Lombards isn't taking into account that the Lombard migration into Italy was not an entire monolithic ethnic nation on the move. This migration/invasion/settlement consisted as much of members of other Germanic tribes as much as it did former "Roman" (whatever that word meant at the time, which is a separate argument) soldiers and settlers from other regions. So because this was a roving alliance of soldiers/settlers/opportunists rather than a tightly bound tribal nation, the numbers could be significantly lower than 200,000.

What was clear however, is that once they moved into the ravaged Italian countryside, they quickly took over many of the elite positions in that society formerly held by whatever survived of the Roman aristocracy. There are records (certainly biased, but who isn't) of the Lombard leaders seizing land and killing rich Romans to take it from them, but clearly they didn't kill all the rich Roman landlords. The surviving Roman elite co-existed with the Lombards in areas where they took over control. Because to quote Chris Wickham, "it was better to be taken over than to be fought over."

At this time though, there was clearly still a separation, as there are records stating that the Romans were allowed to live under Roman law (though under the authority of the Lombards), whereas the Lombards were judged separately according to Lombard Law.

From here to the time of the start of Crusader Kings 2's Charlemagne DLC, the situation completely changes.

By the time of the Charlemagne DLC around 769, there are almost no references to anyone being a Roman in the areas under Lombard authority.

"The Romans in Lombard Italy virtually disappear from history, so much so that it could be seriously argued in the 19th century that every one of them was reduced to slavery. Even in the 8th century, when our documentation begins, we find scarcely a reference to them: 3 or 4 citations in the Lombard laws, 2 or 3 in the charters. We tend to refer to all inhabitants of Lombard Italy as 'Lombards'; our evidence certainly allows us to." (Wickham)

So clearly at this point, it's not even 10% Lombard to 90% Romans. It's more likely 90% Lombard to 10% Roman. But how can this be? Surely the bulk of the population remained descended from the people who were Romans, and surely the Lombards can't have outbred or ethnically cleansed the population without it being noted in the record?

From here, the story gets more complicated because now you have to deal with modern theories about identity formation.

This is because modern identity theory isn't about the "essentialness" of an ethnic identity, meaning for example "once a Roman always a Roman." Identity is seen as fluid, and situational, though still respecting that there are real barriers to changes. Because the Lombard elite were the ones who held the power, it was in the interest of those who wanted to seek power to play the political game in their court, adopting Lombard mannerisms, adopting their language, etc. And of course for the peasants, they would readily adopt the identity of their lord because they didn't have much choice for alternatives. Consider how much of your own modern identity is a product of constant cultural reinforcement, propaganda, and education. If a peasant isn't exposed to constant reminders that s/he might "need" to continue being "Roman", why would they, especially when the alternate Lombard example is right there?

This is reflected across post-Roman barbarian Europe, in Gaul for instance as you see the shift from Roman/Latin names to Germanic ones, from a population that is clearly descended from the Romans, so Lombard Italy isn't an outlier.

So to answer your final question, who are modern italians descended from? Well they're descended from all of these identities, but these identities are just temporary labels in time. If you were to do a genetic examination of the Italian population (much like they did with the British population), you'll find that despite the constant influxes of other identities and DNA, that the bulk of the DNA represents local DNA.

Meaning, who are the Italians descended from? Mostly the people who lived in Italy. It's just that at different points in the history of the Italian peninsula, the people who lived in Italy called themselves different things. But the bulk of the people themselves like the peasants and your average joes, genetically speaking, have always been there.

Sources:

• Christie, Neil. The Lombards: The Ancient Longobards. Oxford: Blackwell, 1995.

• Wickham, Chris. Early Medieval Italy: Central Power and Local Society, 400-1000. Totowa, NJ: Barnes & Noble, 1981.