The thinner oil based lubricants and water displacers are fine. I don't notice a difference in cutting speed with them vs. water, but they do have some improved feel in terms of action and they don't dry off as quickly. Can't flatten a water stone with one with oil on it, but it's easy enough to wash it off.
Oil would be OK in a film - it just needs to be thin enough that the diamond will penetrate into the oil.
I recall reading years ago that water displacers like WD40 can't be used on stones because they leave a film that will build up, but it's not the case. It may leave a film over time, but honing on a diamond hone will remove it (the rubbing of the tool will).
re: custard's post above, I still have some of the ultex stones, and use one sometimes for setting up kamisori that I've reground. They're usually close to untempered and the hone works well for that. It's slower and more tired, but that's true of all of them. I still have the two atoma plates I bought probably 12 years ago now, they're slower, too - the only reason I'd go for the cost level of them would be for flattening stones. The ultex types can be hollow or a little bumpy, but for typical sharpening, that doesn't matter. I'd summarize them as being absolute dandy stones for what is $15 to $20 in the united states, easily equivalent to DMT's duo and dia products. If they don't hurt the edge of a kamisori, they won't hurt the edge of anything. I prefer them when they're a little worn. If an edge is too far gone for one to refresh it, crystolon or india is a better option. A good friable crystolon stone will cut anything, including the really absurd powdered wondersteels like S30V and SGPS.
At any rate, I would think a $20 two sided ultex stone would hone bevels and do minor honing on backs of tools for a decade no problem. Maybe three. For back flattening of poorly made tools or older tools, PSA al-ox paper on glass. 10 times faster, and cheaper, too.