Oneworld.com will tell you your options. To the extent there are multiple, you should use the search function on this site and look up each of the specific airports.

But no one can really answer the question without knowing what airlines you are flying. You probably don't have any options, though.
If you are flying BA from JFK to LHR, you'll be in terminal 7, and have access to the BA First Lounge.
If you are flying AA from JFK to LHR, you'll be in Terminal 8, and have access to the AA Flagship Lounge.

At LHR, if you are flying BA, you will be in Terminal 5, and the only option is the BA First Lounge.
If you are flying Qantas, you will be in Terminal 3 and can choose between the Admirals Club, the Cathay First, and BA First lounges.

From DXB, if you are flying BA, you will be in Terminal 1, and have the BA Galleries Lounge.
If Qantas, Terminal 3, Emirates First Lounge.