It's an arguable (and much-argued) point. There are 19 European zoos (including Port Lympne) maintaining 'Barbary' Lions (there's a list here: ZootierlisteHomepage). These are all descended from various animals found over the years to have Barbary ancestry (most famously from Rabat Zoo). How pure they are is where the debate lies - a few years ago the whole programme seemed about to give up and just admit they weren't pure enough for it to be worth it - but it seems to me there has been a bit of a resurgence the last few years. So - there are animals labelled as Barbary Lions (Panthera leo leo) in zoos - but for now it's an open question whether they are 'proper' Barbaries. But to me, it seems reasonable to keep them going until they are utterly disproved. (of course, this is complicated by the new 'there's only ever been two lion subspecies' theory, but that's a whole separate debate!)
It seems to keep going because every so often, despite any scientific evidence to the contrary as to their purity, a new zoo or two gets into keeping 'Barbaries' e.g. Belfast and Hanover both have stock from Port Lympne, while Port Lympne are currently not breeding any.
Such a shame so much is now off show at Port Lympne. Their is now no entry to the old meerkat enclosure, samaira the babary lion, Blizzard the snow leopard, the 10 scottish cats and the walkway to the cheetah exhibit