The first thing to do is make sure the teeth on the rasp are as clean as possible. You can use either the brush on the back of a hoof pick, or a wire brush to scrub between the teeth. If you start working on the rasp without cleaning it, then you may probably end up just wasting your precious time, as the lubricant that you will use will have least affect on surface of the rasp teeth.
Now you need to take a small amount of WD-40 and apply it to both sides of the rasp. WD-40 is a great stripping agent, and works really well on steel. Applying it on rasp will prevent the steel from rusting. While applying WD-40, make sure you cover all the areas of rasp so that there is no risk of corrosion initiation from any part of the object.
After lubricating the rasp, you can wrap it into a cotton towel and store it on a shelf in your tack room. You can use any of your old cotton towels for this purpose and save money rather than purchasing a new towel.