I've used water for a long time or just dry, tried WD40 for a bit, now mostly use mineral oil.
From the DMT FAQ:
While we recommend you use DMTŪ products dry or with water only, it is acceptable to use a variety of lubricants when sharpening with DMTŪ products. Mineral oil, mineral spirits, kerosene, WD40 can all be used without harming your DMTŪ sharpener.