Hi frequent flyers, due to some schedule changes I ended up with a ticket that looks like this:

YYZ-DFW on AA - Economy Y
DFW-HND on JL - AA codeshare Economy Y
HND-HKG on JL - no codeshare Economy N departing the next day

(AA ticket stock if that matters)

I know Y ticket would get me lounge access but since my ticket is not the most straightforward I rang up JAL. The agent sounded confused too over where/if I can access any lounges during my trip, and after a few minutes hold he told me I can use the lounge at DFW and HND but only on the day I arrive, not when I‘m departing again the following day. This didn't make much sense to me. If anyone has been in the same position before or has any insights, or if we have a lurker around, I’d much appreciate if you could shed some light on this, thanks in advance!