IME state the following - "
Virgin Australia is NOT a member of Skyteam, it is a joint venture partner with Delta and Skyclub, and lounge access is based on Skyclub rules NOT Skyteam rules, can you please check on your computer or call your supervisor?" Only had to do it once, took quite a few key strokes from the agent but I got in (can't remember where it was).
FYI: Skyteam rules (unlike oneworld) prohibit status based lounge access to ALL (not just N.A. card holders) on domestic flights, which is why many DL lounge agents
automatically say no - not realising that the VA/DL joint venture is different, but after a few clicks, their computer systems will advise them so!