What if the Lombards don't invade invade Italy?
The Byzantines would be likely in charge more longer, but they would be still in crisis, and anyone with a bit of ambition would use it.
The most likely candidates :
1)Franks. They already raided Ostrogothia and Byzantine Italy, in the north. They know the country and they would be able to take the north.
It would have very interesting consequences, with Franks having since the beggining mediterranean strong bases, they could manage to put an hand on the western mediteranean trade and to control all the way between Italy and Frisia.
If the Arabo-Islamic conquest still happen, they would maybe be more strong and able to resist naval raids. At the end, Francia could look a bit more like Byzantium.
2)Arabo-Muslims. While we're talking of that.
If the largest part of italy is still under the Byzantine more or less declining control, they could be more interested in conquering Italy rather than Spain.
Critically if they fail to conquer the Berbers at the contrary of OTL, conquering Sicily and then southern Italy is really doable.
3)Exarchate. Ok, a bit of cheating, but it's not unlikely that an ambitious exarch would take opportunity of the problems of Byzantium to just take over Italy for himself. With the possibility to make the pope "his" patriarch and managing to create something bastard between OTL Ostrogothia and Byzantium.
These 3 possibilities aren't even excluding each other.
What if they get conquered by the Avars?
1)More tardive and less formation of Slavic peoples. According to Peary, the crisis of Avar Khanate allowed the slaves they were in their domination and at their periphery to take opportunity to free themselves. By making that, they would have began the processes of "national" formation.
Without Avar to gather slavs, you probably wouldn't have Croats, Slovaks, Slovenians. Slavic minorities, maybe, but mixed with germans and the old roman background.
2)Probably earlier christianisation of Pannonia.
3)Avars became christianised quickly, and abandon as well their more distinctive customs. After 2 generations, "Avar" is not for ethnic people but only for naming the ruling elite whatever from barbaric or roman origin.
What if they migrate into Dalmatia and the western portion of the Balkan peninsula like the Slavs did in OTL?
The problem is the Slavs did it because they're fleeing Avaria.
All depends of the date. If it's before 600, they settle Dalmatia, christianize themselves and you'll have a Bulgaria-equivalent instead of Yugoslavia (to resume, a slavic country named Avaria).
If it's after 600, it's incredibly more hard. Not only they would have a strong resistance from slavs, but they would have been more vulnerable to frankish and byzantine attacks.