DO NOT USE STRAIGHT MINERAL OIL as "honing oil." Straight mineral oil is too heavy and viscous.
First, make sure her stones are oilstones and not waterstones, and that they're already oily.
If they are oilstones, and already oily:
One doesn't usually seek out "honing oil" at a restaurant supply. Nearly all hardware stores carry pre-mixed honing oil, usually "food grade." It's good stuff. The smallest amount is enough for many sharpenings, and farily inexpensive. Plus, giving her the remainder of the tin (or bottle) when you return her stones, would be a nice way to say "thanks" to her for helping you out.
It is, however, very easy and thrifty to make your own. It only requires two things, mineral oil and kerosene (or mineral spirits). Since each has so many other uses, they make good purchases.
Use unscented mineral oil from the pharmacy, and mix it 50/50 with the kerosene or mineral spirits.
If her stones are not only oily but black with steel filings (swarf) from previous sharpening sessions, you'll probably want to clean the stones before using them. Use a brass or steel bristled BBQ brush. powdered cleanser, plenty of elbow-grease, and just do the best you can. Rince well, and you're good to go.
A little oil goes a very long way. You want just enough so that it "gooshes" when you press your edge to the stone; just enough to you get a micro bow-wave as you sharpen; just enough to see the swarf-laden dirty oil move as your knife traverses the stove. Most sharpeners use too much.
The purpose of using oil is preventing the stone from clogging with swarf during the sharpening session. It is not to lubricate the stone.
If her stones aren't already oily:
Forget the mineral oil altogether and use water as your only lubricant or sharpen dry. Don't screw up her stones with oil unless she uses it; getting the oil out of a stone is a royal pain.
Each of the three methods suitable for "oilstones," oil, water, and dry, each has its own benefits and drawbacks. In my opinion dry is fastest and gives the best results. However, since you're still at the "borrowing" stage, you're stuck with whatever she does.
Waterstones require an entirely different prep. Soft stones with clay binders need to be well soaked; many harder stones with resin binders are splash and go. In any case, you should call her.
I'm a good sharpener with loads of experience, who uses nothing but oilstones -- manmade and Arkansas. But I chose them for nostalgia, not practicality. Waterstones are much faster and more versatile than oilstones, at the cost of a little extra maintenance. When it comes time to buy your own kit, buy waterstones.
BDL