[i]This doesn't apply for Shimano sealed BB's in which case they are both effectively fixed cups. [/B]
How could one adjust the bearing preload with two fixed cups? The only systems I have seen use a fixed cup on the drive side and an adjustable cup-plus-lockring on the left side or a pair of adjustable cups, each with its own lockring. The latter configuration allows the user to adjust the chainline a bit, if necessary.
Look at your right-side cup. If it has a flange that tightens against the BB shell, no lockring is needed (or possible). If it is threaded all the way, with no flange, as on most left-side cups, it needs a lockring.