Lauma analysis (consulted the English and Lithuanian wikipedia pages for this. I tried with the Latvian one but...
Where is her name from?
*Lauma (Latvian)/Laumė (Lithuanian)/Łauma (Yotvingian) (https://lv.wikipedia.org/wiki/Lauma) - fairy goddess or group/type of fairies in Baltic mythology. Descended from the heavens; intermediaries between heaven and earth. Could bring blessings to the people (especially young women with unfortunate life situations) or ensure their doom and punishment. Afraid of metal, esp. iron; and flax seeds.
What are they associated with?
Nature - namely trees such as birch trees; this tree fungus thing (https://lt.wikipedia.org/wiki/Raganų_šluotos)? that's named after them, columbidae birds - so doves and pigeons; rainbows
Water and rain - would show up near bodies of water and take care of them; and summon rainy weather and storms via dance, especially during the new moon or full moon
How do they look? How are they depicted in art?
Could transform into various animal forms, with one of the possibilities being their lower body potentially being that of a chicken's. In full human form would be very beautiful. Depicted with either exquisite clothing or naked.
Anything else?
There is also a Melusine named Laume in Genshin and I think that's really neat.

I think Hoyo did a great job with Lauma. Though I'd prefer her top/shirt being a bit different, overall I really like her design and vibes and how she connects to all of this through being a Frostmoon priestess with a centaur transformation (and maybe a potential Lunarbloom reaction enabler?)
That aside, feel free to ask and I'll try to find more details but overall I think this sums it up enough.