I just spoke to Emirates Reservations CSR and he said even though I am flying J class JFK-DXB, I am not eligible for access to Lounges at DXB because next leg of my flight is not J class. He emphasized that I will have access to lounges at JFK because my flight is J class.
He also stated that I will not have access to DC because my layover at DXB is only 7hr/ 10min. According to him, minimum layover time is 8hr to qualify for DC.