ohhh that's such an interesting question!! i gotta think about this deeply hmmm

i think a big factor in it is that he broke traveler's trust by not telling them he's Fatui. at that point the crush is probably still developing, but when traveler shows in the Meropide arc that they still don't trust lyney and keep him at an arm's length, lyney probably feels that his crush is and will only ever be unrequited. of course feelings don't just go away, so he probably ends up pining after them until well after that arc, only fueled by the way the traveler stood up to wriothesley for him during that confrontation. as the prophecy arc continues, lyney keeps ending up having to work with the traveler, and i bet seeing traveler's infinite kindness is like a punch in the gut for him. even more so that even with that kindness and compassion, it seems traveler can't really see past lyney's Fatui status, and that probably eats away at lyney over time.

a common headcanon is that wrio and lyney end up working together a lot during and after the prophecy's passing through some kind of Fortress/Fatui collaboration event, and i think it's in those moments that lyney and wrio come to see eye to eye a bit more. while traveler tends to enable lyney's masked behaviour, wriothesley keeps poking and prodding at lyney's mask because he's seen lyney without it before. being ~seen~ isn't something lyney can fight anymore with wriothesley, so he doesn't, and the fact that wrio doesn't seem to judge him just for being a Fatuus probably helps ease lyney's heartache over the traveler. the more time they spend together, the more at ease they are around each other and the friendlier their banter becomes. then arle's sq events pass, and the way traveler ended up involved i think shows that their stance on the Fatui as an organisation shifts a bit and takes on a more sympathetic angle, and having the traveler fight alongside lyney brings them closer together again. when all is said and done, lyney desperately wants to talk to someone to process what he went through with his siblings and his 'father', and while it would make sense to talk to traveler bc they witnessed everything, lyney finds he wants to tell wriothesley more than anything. i think it really soothes his heart to have wriothesley listen attentively as he recounts the story, to have wrio tend to the wounds he sustained during his fight and let him stay to rest for as long as he likes.

eventually the time comes that traveler continues on to natlan, and as lyney and his siblings send them off it hits lyney that he's mostly gotten over the traveler. he's not sad that they're leaving, he's not still bitter about how their falling out went down, he just... wishes the best for them on their journey and hopes they come back to visit sometime. he finds himself visiting wriothesley more and more outside of their collaboration meetings because he feels safe and seen around wriothesley and likes talking to him and bantering with him. maybe there comes a moment where they accidentally end up in a physically close position, and they have this awkward moment where they feel they should move away but also don't really want to. the way lyney feels flustered about being so close to wrio probably breaks it to him that the object of his affection has properly shifted. I'm sure it throws him off, mostly because while the crush on traveler had been almost instant, his feelings for the duke developed way more slowly. of course he had a grudge and a broken heart to work through, so that's why the crush on wrio ended up sneaking up on him. i think he has a genuine freak-out about it, overanalyses his thoughts and feelings until it drives him insane. his crush on traveler had barely even formed before its potential to evolve into something more got shattered, so he never really had to reckon with the prospect of Being With Someone. now that it's, like, on the table again, lyney really stumbles over things like love and intimacy and vulnerability and his future and how he doesn't actually know how to deal with such things. it might cause him to just keep his feelings to himself until he "figures them out", except he never really does because feelings don't work that way. whether wriothesley notices and/or reciprocates is something i will leave up to your imagination for now... 🤭

man this really made me want to see a scenario in which lyney and wrio end up in a fwb kinda situation to try and get over their respective crushes (who wrio is pining over is up to you lol) and eventually fall for each other, that would be super tasty 👀 but thank you for offering me this question to mull over, i had lots of fun figuring out how i think the scenario would unfold 💕💕 if you have questions or different ideas feel free to reach out to me again, i would love to know your take on it!!!