Normally 8x57JR or 8mm Mauser (rimmed or flanged). Later manufacture may have switched to the 8x57JRS chambering.

Never heard of one chambered for the Austrian cartridge, which is mainly used in Mauser rifles, Mannlicher Schoenauers, and straight-pull Steyrs, but anything is possible I guess.

Normal Lee Speed 'factory' chamberings were .303, 7x57R and 8x57R, .375 NE, and the .405 Winchester. If the 8x50R was ever an original BSA factory chambering, it appears to have escaped the historical record.