I doubt that the flights will update by the time you get to JFK but you will have lounge access based on your tickets for the outbound.
I calculate that once you get there you will have (90)+40+210+140+210=690 TPs. I went to Hawaii on an itinerary that was ticketed by AA (much cheaper than BA for the same itinerary) and the flights posted in 3-4 days so you should be OK for lounge access on the way back.