At the risk of pointing out to the obvious, when lounges for J and lounge for frequent flyers are differentiated in Europe, it is in fact the frequent flyer ones who tend to get the better one (see Senator lounges vs Business lounges on all LH group airlines and in fact most other *A equivalents). In some other parts of the world, things are different (e.g. QR, who keep better lounges for J over frequent flyers), but Europe is BA's competitive field here. And as mentioned, any differentiations would likely be about downgrading rather than upgrading.

That said, I'm also unclear what's the basis to suggest that CW is not competitive right now? J is simply packed on almost every flight, to the point it is extremely hard to get I or R availability let alone award space long haul, Club Suites are being a big success and BA is ahead of AF again on that (though AF is following suite) and miles ahead of LH on comfort (again, those are the two competitors for the global European market). Don't take me wrong, I always enjoy product upgrades, but it's not clear to me that BA "need" better lounges from that point of view.