I don't particularly think Lotharingia is terribly plausable as a kingdom. It only existed from 855-959, had no particularly stable borders, and no defining features or culture. After it's division, nobody ever pretended the title. The Kingdom of Burgundy itself was at least nominally a title from the fourth century until 1378. Charles the Bold was to be crowned king of Burgundy by the Holy Roman Emperor, not Lotharingia. The Duchies of Lotharingia were entities that the Empire had spent centuries dividing and dismantling. The Emperor would have had no interest in allowing it to consolidate under an independent ruler. The de jure of the Kingdom of Burgundy on the other hand, was pretty much entirely controlled by France, and the Emperor would have had a strategic interest in seeing France lose territory
A more realistic idea would be to have an event or decision to "Form the Kingdom of Burgundy" which would give claims (or cores?) on the former de jure of the Kingdom of Burgundy in France, if your relations with the emperor are good enough.
I do think that a Rheinland unification would be nice however, but not for Burgundy.
You should look at the Trier Conference of 1473, even if the kingdom offered to Charles the Bold was not name Lotharingia, it was, de facto, this kingdom. The ambitions of Philip the good, and then, Charles the bold, the last dukes of Burgundy, were indeed to form an unified kingdom with all their principalties. The fact is that, in EU III (edit: and EU IV too) , Burgundy is represented as one unified state, which was not at all what historically happened.
Imo, Burgundy should be showed, IG, as a lot of PU's between the duke of Burgundy and other opm principalties, and the goal of the burgundian player would be to unify all of these principalties inside the same state. Lotharingia is a name that could be changed anyway, the fact is that the dukes of Burgundy wanted to become the kings of an unified, and independant state, whatever its name is.
