What is the name of the ‘up arc’ ornament on the first note in this score? Then 
I’ll look it up in the LPNR.




That's a Scoop.  I don't think LilyPond supports it directly, but several ways 
of faking it are shown in this thread (two links to different ways of viewing 
it):
https://lilypond-user.gnu.narkive.com/nbjxGoSy/scoop-before-note
https://lists.gnu.org/archive/html/lilypond-user/2021-09/msg00429.html


Paul

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