Hey Marbles - I doubt that 3hrs is enough for the BA system to update you from Blue to Silver. If you are flying Club to JER then your boarding pass may given you access at LHR because you arrived inbound in business (Im not 100% sure but someone else probably knows the official answer).

Another thing to be aware of, once you move to silver your tier points are reset and your first leg of your NY flight will also reset. I just moved from Blue to Silver after doing a domestic AA flight in the US, however although my outbound flight gave me enough tier points to move to silver - 4 days later when i did the return I was still showing as blue and when BA moved me to Silver they reset the tier points for both the inbound and return.

However when you leave NY you should be silver by then and can use the lounge at JFK.

Chessy