Here's a thought: Lance although cocky about his looks is low key self conscious of himself so Keith gives him little butterfly kisses all over while telling him why he's beautiful and special.
Lance has a strict skin care routine, and he wouldn’t let menial things like living in a ten thousand years old alien castle ruin it for him.
He’s found things that suggest alteans too care about their beauty, and skillfully used his resources to put up a fight against dry skin and dirt. The fact that he also found a literal giant bathroom full of cosmetic products inside the Castle helped, too.
Keith, actually, couldn’t care less about all that. He’ll wash himself if needed, and that’s it. But it’s nice to bathe with Lance, and to feel gentle fingers applying masks on his cheeks, touching the slope of his nose, slow and wondering, even if Lance sometimes likes to call him “greasy boy” and makes him wash his hands in weird occasions.
Lance also doesn’t talk about his problems, if he specifically doesn’t have to address them, but Keith is more observant than you’d give him credit for.
The baths are already enough of a telltale - because for all his boasting, Lance seems to be unable to look at him, keeping his mouth stretched in a big grin and his eyes downcast, his stance weirdly rigid and the pitch of his tone a little off. Only when they’re fully submerged he seems to gain back his ability to snark him to death and Keith is glad, but piqued.
He brings it up on one of the night where Lance is loose, and happy, talking a mile a minute in that chatty, endearing way of his, making every dumb topic seem vastly more interesting and exciting than it should really be. In one of their bored strolls through the Castle, they found a room with glass walls, overlooking the immensity of the universe around them, and now they come here late at night (they think it’s night, anyway) to watch the stars. It’s cheesy, but whatever.
I wonder if Tae developed the messing with JK’s hair thing because it used to (or still does) calm the bun down or help him when he’s shy or awkward. JK messes with his own hair when he’s nervous, so…?