Lotharingia overall was a pretty stupid idea on the part of the sons of Louis the Pious. It simply had too long a border to defend for the amount of land contained within those borders.
Regardless of who rules the Middle, East and West are guaranteed to be the stronger powers: the West contained all of the Frankish heartlands apart from a few scraps near Aachen, and the East was pretty much a new identity from the old Empire, having discarded partition inheritance and also had the advantage of being FAR away from the Vikings.
Lotharingia simply fell to the same issues that plagued the Merovingians. They had no real power, as the West and East controlled it. Every time they had a strong ruler (which the two they had were certainly not), his achievements meant nothing when the realm balkanised on his death.
So, if Hugh gets in power. Well, in OTL Hugh was recognised by his people as a tyrant. Having the stain of bastardy would not help him, even if he had been legitimised. (Kind of like the debate as to whether Charlemagne was a bastard!). Charles the Bald especially had been trying to reunite the empire a bit, so I would deem an invasion likely, probably no later than 875. When Charles dies (877), his son Louis (the Stammerer), will inherit a nearly-won war, which would certainly enhance his prestige.
The succession in the East was a bit of a mess by this time, so I think they would stay neutral in the conflict. Because Louis was somewhere else, I don't think he would have died as early as 879, probably he could have lived until 900. He would be seen as a relatively 'meh' king, who would probably spend his reign somewhat successfully battling Vikings.
The sons of Louis (Carloman II and Louis III) die the same way and time they did OTL for simplicity, so are both gone by 885. Of course, they were never king and simply get forgotten.
In the East, Charles the Fat will just bumble around until he dies in 888. Louis would be the most likely ruler there if no coup occurs in the east, else whoever the revolutionary is will get the kingdom.
When Louis the Stammer dies, he is succeed by his OTL-posthumous, son Charles 'the Simple' who would get at least 2/3 of a reunited Karling empire.
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Any answer that keeps Lotharingia somehow immune to this type of disaster it became almost certainly butterflies Lotharingia itself. That said, if (by ASB intervention) Lotharingia could magically stabilise itself and not get invaded for 2 centuries, then yes a culture could develop. That always occurs if the same force controls a region for long enough. The trouble is getting that control.
- BNC