I noticed something a little bit strange when I discovered the page to buy lounge access in Manage my Booking.
I have a business class booking through DOH with BA Silver/Oneworld Sapphire status.
As expected the page lists Al Mourjan and the Business Class Lounge as inclusive but also the First Class Lounge, which doesn't match the Oneworld page, which claims it's for First Class and Emerald only.

Could I get in there?

Not that I plan to go there, I might even buy access to Al Safwa.