I know they were a Germanic tribe that ruled Italy, but compared to other tribes like the Franks and the Ostrogoths, I can't find much on them.
There's not as many books on the Lombards in English as compared to the other barbarian tribes. I mean to the best of my knowledge, you're looking at pretty much The Lombards by Neil Christie which was written in 1996, and Early Medieval Italy by Chris Wickham which was written in 1981. That's pretty much it. Wickham's book is still commonly cited even though it's over 30 years now. It probably wasn't helped that the newer Medieval Cambridge History had to skip a chapter on 7th century Lombards due to not being able to find someone with the time to write about them.
In general, this is because they're more of an Italian interest. They occupy the unfortunate "dark period" of post-imperial Italy, between the Byzantine reconquest and Carolingian takeover. People like to paper over the 200 years and pretend nothing happened in Italy.
However, some of this is also because Lombard society was quite closed, and though we do have a set of surviving laws from Rothari in the mid 7th century, that's pretty much it for contemporary accounts, and as you can imagine, it's hard to reconstruct a society on the basis of only a left behind legal code. For the rest of the political/social history, we have to divine from Paul the Deacon, who's writing 200 years afterwards for a lot of subjects. The most crucial period, the transformation of Lombard society from migratory tribe to settled elites in the late 6th to early 7th century, we know very little about. And these are the absolutely crucial years in the transformation of Roman society into "Italian" society.
So back to your question at hand, who were the Lombards. In a nutshell, they were a Germanic confederation that were frenemies of the Eastern Romans/Byzantines, whom in the vacuum of power after the end of the Gothic War, invaded/moved/settled into Italy, quickly taking over most of the countryside of the peninsula, excepting the most urbanized and important Roman cities. In the years to follow, they eventually took over most of Italy, and were only politically destroyed when they were powerful enough to consider taking Rome itself, by which time the pope called in the Franks to rescue him, after which the Franks/Charlemagne conquered and took over the Lombard kingdom.
There's obviously a lot more to the Lombards, and a ton of room available for both analysis and speculation, but I figure if you have any more direct questions, you should feel free to pose them and we'll work from there.
Some other interesting tidbits not mentioned yet:
The word "Lombard" derives from Langobard, meaning "Long Beard".
The Lombards originally came from what is today Northern Sweden, and slowly migrated southwards to Central Germany during the height of the Roman Empire. As Rome declined and the barbarian migrations became more fervent, the Lombards fought their way into what was once Roman Noricum and Pannonia in Late Antiquity. There, they were instructed and paid by the Byzantine Emperors to fight off the Gepids. The vulnerability of Byzantine Italy after the Gothic Wars and the Plague of Justinian allowed them to cross the Alps virtually unopposed and permanently settle the Po River Valley in the mid 6th Century.
There were three principal Italian Lombard states during the height of their power (roughly 6th - 9th Centuries), the original Lombard Kingdom of Italy, which ruled most of Northern Italy from the mid 500s until its collapse and subjugation by Charlemagne in the late 8th Century, and the Duchies of Benevento and Spoleto, two breakaway factions which established themselves in defiance of the Byzantine Empire in central Southern Italy from the mid 7th Century until their demise in the late 9th and early 10th Centuries.
The city of Campobasso, as well as many surrounding towns in the present-day Italian provinces of Abruzzo and Molise, were founded by the previously-mentioned breakaway factions of Lombards who fled the Lombardic Kingdom in Northern Italy and founded the Duchies of Benevento and Spoleto in the mid 7th Century. At the time of their arrival, almost the entire region had been depopulated from centuries of barbarian raids and administrative neglect.
Although Lombard rule would eventually collapse, significant groups of people who identified as Lombards persisted past the turn of the first millennium. The Byzantine theme of Langobardia, formed sometime after the AD 873 reconquest of Bari, interestingly retained the name of the old region of Langobardia until the collapse of Byzantine Italy in AD 1043. Additionally, a number of Southern Italian successor states which claimed Lombard descent, can probably be seen as evidence for a persistent Lombardic presence in the South until the conquests of the Sicilio-Normans in the late 11th Century.
Though obscure, there are several Lombard primary sources that have survived to the present day. Of these, the best known is Paul the Deacon's Historia Langobardorum. Although many of the major cities, including Bari, have their own city chronicles dating from the period as well, they remain poorly studied.