I don't have any inside knowledge of BP, but I believe both of those refineries are setup to run Canadian Heavy oil, which isn't usually used to make lube stocks.
I wouldn't also assume that BP even refines the oil that goes into their two cycle oil. The co pany I work for has several refineries and we don't refine a single drop of lube stock. We buy it from others and blend it with additives bought from some other company.
If you guys realised how small the lubricants industry is it would probably supprise more than a few. Mobil for instance has the market cornered on certain weight esters and PAO's. Where do you think Amsoil buys their stocks from?? And that's just one example.