JFK Clubhouse access

Hi everyone
I have been a lurker for a while and a fairly regular Virgin Atlantic flyer. Have been silver for several years, on and off, but never quite made it to gold.
I have a question that I hope the collective knowledge of the forum can help with because I can't find a definitive answer elsewhere.
In a couple of week I am flying LHR - BUF with a connection in JFK in Upper.
The LHR-JFK flight is Virgin and the JFK- BUF flight is Delta, but all booked through Virgin on one ticket. The domestic flight is 'first'. Both the inbound and outbound flights are T4.
The connection in JFK is about 5 hours. Can I use the Virgin Clubhouse during this connection, or do I need to go to the Delta lounge?

We had a flight back in June, lhr-jfk upper on virgin then jfk-mco on delta first, all booked through virgin, our connection was also through T4, we went to the virgin lounge by gate A5, the guy on the desk just wanted to see our first leg ticket ( lhr-jfk) plus our onward leg ticket to MCO, didn't have a problem getting in. wanted to try jfk lounge as our return two weeks later our connection was only 60mins so had no time

That's good news. I have the same issue on the way back.
Excellent, I'll give it a go