When lapping stones you do not want to use it dry, the build up of loose grit rubbed around on the DMT will eat the substrate that holds the diamonds.
All diamond hones and some ceramic too is more like "can be used dry".
It is very seldom good for them and since you get no lubrication from either water or oil, it's not so good for honing steel either.
I had some rust on my DMTs when I forgot to dry them and left them on the kitchen sink, any contact they have with a nobler metal will make them rust faster...