Have you ever seen such a display?
I have, yes, every now an then. It does happen. I always assume the limit applies to all lanes.
Leaving aside where motorways diverge (and I think even then all lanes would be kept the same until the divergence was complete)
They do show different limits even before the physical divergence, though the lane markings clearly show that some lanes (with a different limit) are about to do so.
Back in the '90s when VSL were first introduced, it was suggested that different limits could apply on each lane, but I don't think this was ever actually implemented.
Any limit displayed previously remains in force until the driver encounters a sign displaying something else (a different limit or the NSL sign).
Unfortunately it also happens that there is not always an NSL at the end of a variable speed restriction. Could be because the restriction you last passed has been lifted and so all the signs are now blank, or some other random reason. One simply has to assume after a couple of gantries that NSL now applies (whether rightly or not).