Any chance your flight is Delta-marketed even though it is VS-operated.
Technically if it is, your Delta Reserve gets you into the AMEX Centurion lounge. The nuance here is annoying and unfortunate in this case until VS becomes part of SkyTeam
The Card Member will have to present his or her valid Card, same-day boarding pass, and a physical government-issued I.D. for lounge access. Delta SkyMiles® Reserve Card Members are only eligible to visit The Centurion® Lounge when flying on a same-day Delta-marketed or Delta-operated flight and eligible lounges only include all Centurion Lounges located in the United States, Hong Kong, and London.