Like a couple of others here, I fall into the Venn diagram section "yes, I've heard of LMB, no I haven't read all her books". Actually, I've read one (Vorkosigan) novel but wasn't massively enamoured of it. This story I did enjoy, a lot. Not a "Wow! I must go out and buy all the others" lot, but I did enjoy it.
So, the pilot-narrator that psyque had a hard time understanding... I recognized a relatively common SF trope done well. The ships are controlled through a neural interface by surgically enhanced pilots, which is bound to have some psychological effect on them. Here we see it as part of the world-building, a low-key background presence. We may reasonably expect to find him hard to understand, but since he actually wasn't the protagonist that's not a problem. As a foil to the medic's attitudes, an observer through whom we see her, he worked well. That said, he was a tiny bit quick to leap to the "lesbian necrophiliac" assumption. I'd realised who that final body was before then. But that's a very minor quibble.
The medic's motivations - her extreme care and reverence for her subjects, emphasised by what we don't know at first but clearly also part of her character - and her actions were just right, beautifully portrayed.
The examination of culture, people and traditions was good too. I'm not as immersed in that scene as smithmikeg so it didn't have quite the same resonance, but it's always good to see done well. Some of the best fan-fic I've seen was written by people for whom that's their thing, and in a minor-characters spin-off like I get the impression this was (though as I said, I don't know the universe) it works really well. I did get a slight feel of author-does-fanfic-of-own-work, in fact, but that's not in any way a complaint or criticism. What I mean is that it felt like an exploration of a tiny little corner of no importance to the great story arc - wonderful detail for those whose devotion to the whole may be mistaken for "cult-like", an interesting and very enjoyable stand-alone for the rest of us (assuming it's done well, which this absolutely was).