It happens, even in AHA, but since grey is soooo common in Arabians it's not maybe real prevalent.
I checked from 1985 on up. There are also 670 grey mares with the prefix LA in front of their names. I checked that way too and looked in case she might be a 1/2 Arab. Zip all around. If you can get any more info, I'll be happy to try again and see if I can get any further. The closes I got was La Isla something, was thinking maybe they called her La Izzy, but she had no white on her legs at all.
I was hoping that the NV might be a clue because the person I know that owns a well known stallion with NV in front of his name is a fairly large breeder and has a bunch of broodies. The stallions breeder has been around since the 70's at least, maybe even the 60s and they've owned/bred a lot of horses and I found a couple they had bred with the LA prefix on them, but not anything close to LA Lizzy, Elizabeth, Lisabete or anything like that.