This is a very interesting thread as lounge access rules seem to be somewhat confusing. As Dave Noble noted there seem to be rules specific to the single lounge when you check the OW website. For example, the directory shows 10 lounges at LHR but the logos of different airlines appear next to them giving the impression that only passengers travelling on those airlines would be admitted to that particular lounge. What is more confusing is that this is not clearly stated anywhere. From reading the general rules I would expect to be allowed entrance to any J and F lounge as OWE - but now I'm no longer sure. It would be great if someone could clear that up. Thanks!
When a lounge is owned / operated by a OW carrier, it should open itself to all EMD, SPH, F, and J pax on any OW carrier (during its opening hours, of course). The only valid excuse, I believe, would be due to capacity constraint. That being said, some lounges, especially BA ones, tend to abuse the capacity excuse. Lounges operated by third-parties are only open to pax travelling on the specific carrier whose logo is shown on the OW website.