No.
You booked a ticket premium economy Chicago to Tokyo, and Economy Tokyo to Manila.
Booking class doesn't matter in this case.
It is the cabin you are seated in that matters, with exceptions for First class passengers (arriving boarding pass in F gives you JAL F lounge access on same day connections to C or Y JAL flights).
Your question would be answered if you searched, and found this thread.
JAL Sakura lounge access in Japan