Chapter Text
Platonic
She would be wholly indifferent to their sickness, if not curious. Very much of the mindset, "pain is just weakness leaving the body." Someway, somehow, she would even relate TAV's minor sickness to some type of Githyanki trial.
"Gith do not get such pathetic illnesses as weak as this; a Githyanki illness ravages the body and mind, and is in itself a trial, in which we either prevail and come out stronger, or we rightfully die."
Not quite the beacon of comforting words and actions, but as a whole, she's very indifferent to TAV's plight. She might help if they asked her for something specifically, as she does hold a level of respect for TAV, but otherwise will mind her business and do her own thing.
Romantic
If her TAV somehow gets sick with a common cold, Lae'zel would simply tell TAV to get over it.
When TAV does not, in fact, get over it; then she starts to get worried, not that she'll ever admit it (to anyone but TAV, at least). She'd ask them how she can help them feel better, and follows their instructions precisely. TAV would have to reassure her multiple times that it's just a common cold, that they won't die from it; but every time Lae'zel brings them something (soup, a hot drink), and it doesn't immediately cure TAV, she would scowl and snap, saying something like "Why are you not cured yet?!"
Her anger is never, ever directed at TAV, she just doesn't know what to do or where to direct her energy. She's also incredibly gentle with TAV, whenever she has to move them or when she tucks them in, or any physical touch for that matter-- as if she's worried she might accidentally hurt them. Her help and care is very militaristic, with an undercurrent of ever-present, silent worry.