Basically was the society after Lombard conquest in Italy primarily Roman or Germanic? It seems that all the people in Italy were called Lombards.
The latest literature (up to and including including researched published by Massimo Montanari at the University of Bologna in 2015) can only agree that there no real consensus as to how or why the Lombards were able to enter Italy so easily. The Emperor in Constantinople certainly had other fish to fry, while internal instability and manpower problems within the governing administration could have facilitated the entry of a foreign "Warrior Class" which rapidly supplanted the Italo-Byzantine ruling class (much like the Normans in southern Italy five centuries later).
The integration of the Lombards into the existing Romano-Italian society is also seemingly conflicted; simultaneously coming into conflict with the old Roman "Senatorial" class while also being rapidly absorbed into it, by some estimates in less than a generation. In the late seventh century, the "Edict of Rotari" Lombard laws (in Latin) but dealt almost exclusively dealt with the resolution of high level-confrontations, blood feuds, and "Private Wars." By the eight century, Lombards and Latins were indistinguishable.
What is certain is that Italy under the Lombards was extremely politically unstable; the peninsula was divided amongst a number (anything between five and thirty-five) power-brokers called Dux, a latin word meaning military leaders (generally rendered in english as "Dukes") who came into conflict with each other in every conceivable way. Thus the "Lombard" state of Italy was generally characterized by a bizarre cyclicality; after the death of a strong sovereign the Dukes begin fighting against each other, the Byzantine military governors in Latinum and Romagna make gains against the Lombard state, the Dukes see the need to stand together, and rally behind a King. The cycle then repeated at the death of the King.
The seemingly invisibility of the Lombards on Italy's continued heritage is in great part due to the fact that, both physically and figuratively, they continued to make use of many of the old Roman structures. These structures would be either decisively abandoned or modified beyond recognition during accelerated urbanization in Italy starting in the eleventh century. Those structures that the Lombards did construct for themselves are not really all that distinct from late Roman/Byzantine architecture.
There are bits of Lombard heritage here and there if you know where to look. A circular square in the city center of Milan, for example, is called Cordusio a corrupted form of "Curia Ducis" or "Duke's Court." The square, in the dead center of polygon traced by the old Roman walls, traces the outline of an old Lombard Castle.