My mother’s parents came from 35 miles south of your kin – Avigiliano, Bascilicata and always called it sauce!
It seems that “sauce” vs. “gravy” is not regional, as denoted by these 2 Italian families coming from such close communities in Italy, but may have been a translation issue. Italians arriving in America were given differing translations for their Italian "sugo per pastasciutta.", etc. Because the expression for "gravy" in Italian is "sugo d'arrosto", which is literally "juice of a roast, when they said the word "Sugo," sometimes they were given “sauce”, sometimes "gravy?"
Mom’s lasagna, now made by my wife, is similar to yours except:
- No onions in the sauce, but paste is the key to thick sauce!,
- No sausage,
- She added sliced eggs – Anyone else? My wife’s people who came from between Naples and Amalfi coast also added eggs but no meat!
You’ve got me hungry for Christmas dinner – my son will be making our lasagna this year!
Merry Christmas & Happy Holidays, whatever your celebrations, whatever your traditions, whatever you call your sauce.
p.s. Not frying the meatballs is an “infamnia!”

and we mostly had macaroni, sometimes spaghetti, pastina when we were sick but never pasta!