Several sources reference a group of five specially finished 1988 LSCs:

An AOAI discussion specifically asks how many 1988 LSCs were produced with Pearl White paint and black ground effects,
and the correct answer was five.

A later listing for one of the cars describes it as "number 2 of 5 Limited Edition examples produced" and notes the white exterior,
black accents, and special trim.
Another AOAI posting refers to a car as "1988 Avanti LSC Anniversary Edition #4", indicating that at least some owners and dealers
associated these cars with an anniversary or commemorative series.
The broader historical context is also important. During late 1987 and 1988, Avanti was promoting a Silver Anniversary theme
celebrating the 25th anniversary of the original 1963 Avanti. Factory history notes that a Silver Anniversary edition with a
distinctive blackout treatment was announced as 1987 ended.

The best reconstruction from the evidence is:

The five VINs ending 0371–0375 were a numbered run of specially trimmed LSCs.

Their distinguishing features were the Pearl White exterior and blacked-out/black ground-effects treatment.

They were likely marketed internally and by dealers as either Special Edition, Limited Edition, or Anniversary Edition cars,
tied to the Avanti's 25th anniversary celebration.

No found evidence that they received unique mechanical equipment beyond the appearance package and identification as one of
the five cars. The available sources point primarily to the paint-and-trim combination as the distinguishing feature.