Greenwich is open until 1:15am which is more than fine for the current JL3 12:45am departure. There is a gap for the summer JL3 1:40am departure, but the lounge closing should actually work out perfectly assuming the flight is not delayed and boarding starts on time. Of course it is a downgrade if you have access to Soho, but Greenwich really is not that bad. (At least the wine selection is respectable, unlike the hipster selection, to put it politely, in the TYO Sakura lounges.)

Like the reply earlier, I suspect JL will be able to negotiate/pay AA to keep at least one of the lounges open in ORD. Ideally it would be the FL, but at least the H/K AC also has showers.