Both our product page (link) and the VixenCreations website say water-based only, so I'd probably stick with water-based only.
I'm pretty sure none of the material pages list oil based lubes as being compatible. We've used oil lubes with silicone, including Vixskin and O2 with no problems. However, you could also do a spot test to see if any reaction occurs.
VixSkin is 100% silicone, so oil based lubes are not a problem for the toy. Petroleum lubes are not a good option for vaginal use, and they're hard to clean up period (so I wouldn't recommend them for anal use), but other oil based lubes aren't nearly the problem.
VixSkin uses a soft silicone, and the softer the silicone the more points are available for things to bond to, so I wouldn't even try it with silicone lube.