Your canon material for study: 'That Naughty Flashback Scene'
Ready, steady, GO!
For what it's worth, in the present Aaronev seems quite obsessed with Lucrezia. "I will prove that I am still worthy to lead the order! And I will see [b]her[/b] again!" (Emphasis in original.) Whether he felt that way at the time is unclear, but it seems possible at least, and Lucrezia does express (somewhat patronizing) affection for Tarvek before she learns that he's not Aaronev.
The point about Lu using mind control triggers the English teacher in the back of my head-- if this triangle echoes that of the last generation, and they're not going for pure cycle, then they're probably setting up a compare/contrast with the modern being an improvement.
It looks like Lu/Ag might be Love Woman, with the older corrupted by power. (Think kinda like the Mother version-- Archtypical Terrible Mother controls and destroys her children or feeds on them, the good one supports and gives but lets go; Clytemnestra vs Virgin Mary.)
Gil pretty much HAS to be this generation's version of Barry, I'll call them the Idealist, but where Barry is blind, Gil has more savvy.
I think that would put Tarv as the Realist (for lack of a better term), and if we can figure him out, we'll be able to figure out Klaus. My gut says that Klaus's flaw is being bitter, over-generalizing in an effort to be realistic. (The flip side of idealistic.)
Depending on how deep they end up going, I may end up having to get a spare copy of all the books and have my kids write English papers on them....