Will double check again for you and post access rules
From Delta:
Virgin Atlantic Clubhouse lounge access is available at select locations to Delta One™ and Upper Class passengers and Diamond, Platinum and Gold Medallion members with a same-day nonstop transatlantic flight between North America and the U.K. that is operated by Delta or Virgin Atlantic. Diamond and Platinum Medallion members may access Virgin Atlantic Clubhouses in London-Heathrow, London-Gatwick, New York-JFK, Newark, Washington-Dulles, Boston, Los Angeles and San Francisco Airports. Gold Medallion members may only access Virgin Atlantic Clubhouses within the U.S. (New York-JFK, Newark, Washington-Dulles, Boston, Los Angeles and San Francisco Airports). Diamond, Platinum and Gold Medallion members are allowed to bring one guest. While access to the Virgin Atlantic Clubhouse in the U.K. (London-Heathrow and London-Gatwick) is not available to Gold Medallion members, these members may enjoy the No. 1. Traveller Lounge at LHR’s Terminal 3. Please travel with and be prepared to show your Medallion card to the Virgin Atlantic representative to receive these benefits.
Unfortunately I think you're out of luck on the departure route.
VS as far as IK has a partnership with
Delta and Delta only. With no affiliation to Skyteam from what I can tell. On the way back however, you're all set for the DL arrivals lounge

-as well as a ton of skyclubs as you know already.
Was a pleasant twitter convo with you by the way
PS. I'm betting on that you know about Priority Pass. If you have it, there's 3 lounges right in T3 that accept it (being the ServisAir, Air Canada and the No1 lounge). Just thought I'd put that out there