Most anything can be used on diamond hones for lubrication. I've grown to like using a little bit of mineral oil on mine. I'd otherwise be inclined to use something like water, or dish soap + water. But my environment is usually too dry for that, and anything water-based evaporates too rapidly to be very useful. That's why I use the mineral oil, and it cleans up easily with dish soap & water afterwards.
With diamond hones and other stones, I've lately become more aware of how much better the oil works to actually 'float' the swarf, as opposed to using water or anything water-based. I started noticing this on an oilstone that I tried with water + dish soap, and the swarf generated wasn't being picked up with a rag afterward; it was settling more deeply into the pores of the stone and staying there, even while the stone was wet. The oil does a better job keeping it suspended on the surface, and much more of it can be wiped away with a rag afterward, used this way. It's not so much an issue with a nickel-plated diamond hone, as it's not porous, so the swarf is always on the surface, regardless.