Your canon material for study: 'That Naughty Flashback Scene'
Ready, steady, GO!
I'm inclined to believe he really did love her.
First, I honestly doubt Klaus would mess around sexually with a woman he knew a close friend also was crazy for, unless he *honestly* and profoundly wanted her himself.
Second, I tend to see Klaus as just plain honorable in his romances on a more fundamental level: if Lu had been truly footloose and fancy free, with no other complications, and they both were clear on the sex-only aspect of the relationship, then, yes, I can believe it was "just sex." But the very fact that Bill is also involved, and maybe Aaronev, just turns it into a rather nasty game -- abuse of them, if not outright using of Lu.
Third, I read his reactions in canon as being about love, not just lust, pride, or him using Lu. Going by the sad, sentimental viewing of the locket that precedes the Naughty Flashback Scene, to the first frame in which, IMHO, Phil drew him as actually hurt, not just surprised, I read the Fs as walking us into a true heart-ache memory for Klaus, not just an angry one...and not just over Bill's tragedy, which I would expect them to portray differently.
Klaus' first arguments in response to Lu's announcement are that he and Lu are better suited to each other: they are a better couple. He doesn't argue in defense of Bill until Lu's made it clear that there's more philosophical reasoning in her choice than love. His final argument to her is his passion, rather than his dismay over Bill.
Add in the fact that he appears to be a loyal husband now, that integrity does matter to him, and it seems to me very unlikely he was just using Lu as a hot bed-mate: that would be a betrayal of himself, and of Bill, as well as of Lu.
The Secret Blueprints, which aren't canon but are at least an indication of a lot of what the Foglios were offering as the reliable set-up, says that Bill, Klaus and Lu were in a "tense love triangle." Again, if Klaus had been merely messing around with the woman Bill honestly loved, it would be tense, but not really a love triangle.
I find it more disturbing to my understanding of Klaus as an honorable, sensible, decent man to think he'd bed Lu under those circumstances without honestly loving her, or sincerely wooing her, than I find the idea that as a young man he fell in love with a Matahari...especially when Lu's original nature is still unclear, and when Klaus' sense of her acting skills is very high. He could easily have loved in good faith, either because she wasn't the monster we've seen since, or because she -- like Zola -- was just plain good at gulling people, including a younger, less wary Klaus.
I'd rather believe he loved, lost, and learned from it, than think he was just playing a spicy game of lust with the woman his friend adored... even if SHE was that cold, I don't want to believe *he* was. Better a young and loving fool than a young and cynical game player.
Final point, more structural -- but I think reasonably compelling. There's plenty of reason to think that Gil/Agatha/Tarvek is set up to echo Klaus/Lucretia/Bill more than superficially. The core problem faced is supposed to mirror back and forth. At this point it's become clear that in some sense, on some level, both boys do love Agatha, and Agatha on some level loves both boys. For Klaus to not-love Lu, but just be taking what she's giving away for free...while risking hurting Bill into the bargain... pretty much demolishes the mirror.
That can still happen: it can be one of the expected flips the Foglios have planned for us. But at present I'm simply inclined to think that Bill and Klaus both loved Lucretia -- and Aaronev's a bit more of a question.
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.
(Nod) I agree he seemed quite fixated in the present. I have three points that keep me from being at all sure what his original interest was.
He cites his position with the Knights first, and seeing her only second. Oh -- and the lack of indication why he wanted to see her. "I've been waiting to tell her just what I think of her for twenty years," seems possible still.
Vrin's conviction he wasn't loyal to Lucretia/The Goddess, but merely wanted to make use of her.
Last,and for me both creepiest and disturbing, is that Lu was using mind control. We had known about the wasps, and we'd known about the downloading technology of the Summoning Engines. But there are those three tubes down in the Lair. I find it beyond believable that she had tubes and wasn't using them... especially when she is able to comment on the comparative advantages between wasps and mind control tubes. We also know just from her comments that the tubes work just fine on Sparks: she's planning on using them on Gil and Tarvek. Zola is at least expressing a similar type of willingness to tamper when, in her frenzy, she announces she's going to have Tarvek brain-drilled to love her. I am... uneasy... that some of Lu's suitors were unwilling. Klaus seems like the least likely to have been meddled with...if only because he remains "so over her!" Aaronev, with his entirely out-of=proportion behavior, seems the most likely. And, with the novelization coming out, and signs that Bill was going mad after The Fall of the Castle, seems at least possible.
I do think Aaronev looks like a good victim of mind control. He would have to be incredibly, utterly insane with love otherwise. It's one thing to ally with the Mongfish. But he appears to have then specifically handed control of his ancestral orders to Lu, he allowed his own offspring to be meddled with, and he remained blindingly obsessed with her 20 years after her disappearance. I have plenty of other theories -- some which may play well with mind control, some of which may prove to exclude the possibility. But mind control continues to look plausible.
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....