Just a couple of points, Grub screws are indeed available from local fastener or engineering suppliers and are in fact called ‘grub screws’. I buy them for projects from a small company locally and they are as cheap as chips. Set screws are are not another name for grub screws but simply bolts, such as hex head which are threaded all the way up to the head, rather than a short thread on a longer shank as on a ‘bolt’. They all come in socket screw form these days it seems.
Using copaslip is a good solution to the problem of them sticking, Don’t use oil, the screw may vibrate loose. A small tube will last for years if used for it’s purpose. A good substitute believe it or not is soap. Wipe the screw on s piece of wet soap before fitting. That also prevents woodscrews from sticking by the way for those DIY ers out there.
A precautionary tale. I bought an ex school Boxford lathe, in rather good condition as it had little use, a bit bashed but little wear where it counted. However I noticed that the main drive pulley (10 inch dia) was distorted and not running true. When questioned, the workshop technician told me that they had to remove the pulley for maintenance in the past and although they had removed the retaining grub screw it would not shift off the shaft no matter what. he claimed that it ‘must have welded itself onto the shaft’. Eventually they resorted to a hide mallet, hence the distortion.
What they had not known is that Boxford, like many other companies in the past used two grub screws in each pulley boss, one on top of the other. The first one locks the the pulley to the shaft and the second is locked down on top to prevent the first from vibrating loose. Much in the same way that a locknut is used on a screw thread. So, after removing a grub screw always check that there is not another little bugger hiding down there to cause trouble. Before reaching for the biggest mallet you can find by the way.