The OM-2 does have lock-up in a sense - if you use the self-timer the mirror locks up as soon as you press the shutter release, the shutter then opens after the delay. So it's almost as good as a dedicated mirror lock-up function.
I just tried this on my OM2n. It doesn't? If you press the shutter with timer set, the shutter fires as normal.With timer it fires the shutter just as normal after the time.