Yes, but very sparingly. Only use lubrication when a thorough cleaning and a check for interference with wood components have not yielded smooth movement.. We clean our vises at our shop about once a year with a blast of compressed air in the nut threads and along the screw, followed by a very light application of lubricant, usually a dry type lube, such as that used for bicycle chains. Don't use grease, thick oils, or paste wax on the moving parts of the vise. Those products will attract dust and make things worse. Our screws are precision rolled, and thus very smooth and polished. They don't need much lubrication to work smoothly. Keeping them clean is the most important "lubricant" you can use.