Lvtetia is not "the original Roman spelling".
The original Roman cursive spelling is: https://imageup.ru/img224/3989875/roman-coursive-example.png
The original Roman square capitals variant is like this: LV́TÉTIA (too lazy to make an image; I hope you have a serif typeface, it's closer enough)
The cursive eventually evolved into "lutetia"
The square capitals eventually into "LVTETIA"
Later, people decided to use both versions together, using letters like L, V, T, E in the beginning of sentences and names; and letters like l, u, t, e elsewhere.
What happened in mediaeval times is that people decided added lowercase v and uppercase U. So, Lvtetia is ahistorical: it should be Lutetia or LVTETIA or lutetia, since lowercase v is a later invention.
(Similar thing happened when Turkish people devised their Latin script: they divided I/i into I/ı and İ/i. Using Lvtetia is like using Lvtetıa, because Romans didn't put dots over their I's.)
> (edit: that said, when I search for "lugd" I do get search results for LVGDVNO, so maybe the search got improved?)
Yes, I think it has been improved. Thanks!