Are you playing the original release of the game, or DKS / D2:DC? The platforms were modified slightly between D2:ED and DKS.
You should be able to stand by the lever facing where the platforms will appear, (quicksave) hit the lever, quickly jump up both platforms and hit the pressure plate on the second one (I pointed the camera at the plate and selected it, but a couple people mentioned stepping on it, which would probably be faster), drop off and get the chest that appears when the pressure plate is activated.
Ledges in the Orobas Fjords Depleted Ore MinesPlatforms and chest in depleted ore mine.If you can not get it in a few tries, there is only some random loot in the chest (potentially nice in D2:ED; I don't recall it being as good in DKS), so you could easily skip it.