The early Lombard period is difficult to extrapolate datasets for (which normally isn't the case for Italy). I will say that the "Massive Depopulation" narrative is a bit of a contentious topic: There are definetely some cities that declined in this period (Aquileia, Ravenna, Rome) while others were clearly immediately identified as very important by the Lombards (Pavia, Milan, Bologna, and Salerno, while the Lombards also seemed to have an exogenous impact on Venice).

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 Italian administration could have very well facilitated the entry of a foreign "Warrior Class" which rapidly supplanted the Italo-Byzantine ruling class (much like the Normans in Southern Italy do five centuries later).

The integration of the Lombards into the existing Romano-Italian society is seemingly conflicted; reported as coming into conflict with the old Roman "Senatorial" class while simultaneously being rapidly absorbed into it, by some estimates in less than a generation. In the late seventh century, the "Edict of Rotari" codified 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, they were indistinguishable from Latins and "Lombard" had come to mean anything that was indigenously Italian.

My go-to text for the lombards is "History of the Lombards" by Jörg Jarnut, although he tends to be a bit of a catastrophist, contrasting Massimo Montanari's more cautious examination of societal changes under the Lombards.