Your canon material for study: 'That Naughty Flashback Scene'
Ready, steady, GO!
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....