As we say in the engineering world: Yikes!

If both LH and RH cups fit on the drive side then it might be a buggered up (or not) Italian thread. I would take the frame to a heads-up LBS and have them chase the threads with an Italian tap set and face the BB while they were at it. Then you'll know what you have and it will be right. I've had that done around here for a modest charge when I needed to put a modern BB on an old Raleigh frame.

Buona Fortuna