Why do you want to go water free?
Unless your lathe specifies pure oil, or you're machining something where pure oil is a better option (not likely given you're trying to do this on the cheap!), then there's no real reason not to run soluble coolant.

It's worth mentioning, the vegetable based oils will still have additives to improve extreme pressure properties, and also to inihibit unwanted things growing/living in it.