Aspire lounge is not run by a OW airline. It is run by a third party that's contracted by QR to provide lounge service for passengers on its AMS-DOH flight. So if you fly QR J you can use that lounge. Passengers on BA flights are not allowed to use it.

BA lounge is run by BA. As a J passenger on QR you are allowed to use BA lounge even though it is not the designated QR lounge at AMS. OW status is irrelevant as you're flying J on a OW operated and marketed flight.

Having said that, I don't know about AMS specifically but here in the US BA lounge dragons (btw I know we call them dragons but shouldn't they be called dragoness instead? ) have been known to turn away other OW passengers claiming they are at 'capacity'. That's plain bogus but it's been known to happen.

It works the same way at BKK. TG lounges are the designated QR lounges. As J passenger on a QR flight, you can use TG lounges.

CX lounge is run by CX. As J passenger on a OW flight you are allowed to use CX lounge at BKK. I haven't visited myself but if you look at the thread at both QR and CX forum, it sounds like a much better lounge ... so much so that it seems that every OW J (and OW Y passenger with OWE/OWS status) at BKK is planning to descend on that lounge.

So yeah, if you have the time and willing to walk (it is not near where QR gates usually are) then you may want to check out CX lounge at BKK instead.