I had a 3-4 hour layover a couple months back where I flew QR from MNL-DOH in business class then DOH-LHR in economy with separate booking references, the latter booked with points.

I was able to access the Al Mourjan lounges with no issues by showing my MNL-DOH ticket. Just a few phone calls made at the reception but was waved through no problem. Likely to be the case for the other eligible OW lounges if your fare doesn't qualify for Al Mourjan.