I believe "eligible tickets" refers to the SkyTeam lounge access policy that you have to be traveling on a same-day international flight operated by a SkyTeam airline. However, VS has been known to be quite generous to their own elites, so it's quite possible they will let you in anyway.
If you are traveling on an eligible flight, you can also use the Delta Sky Club in T4 (or the Sky Club Express).
Note that you will not earn Virgin Points or Tier Points on a DL E fare.
Thanks for that. The language on the VS website says Golds get Clubhouse access when flying on DL; there's no mention about having to fly international. This was obviously written in prior to VS joining SkyTeam. I know the SkyTeam rules say Elite Plus only get lounge access when travelling international, but I'm curious if VS Gold still get Clubhouse access when flying DL, even when not flying internationally (i.e. as it was prior to VS joining SkyTeam).