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As a 7x Mini-Lathe owner, I have fought problems like you describe many times, and there have been many sources of those problems.If your lathe is similar to mine, I would like to suggest that the easiest way to get access to several of the areas you may want to check, clean, or adjust is to remove the carriage.Remove the tailstock. Then take off the bracket that supports the tailstock end of the lead screw and crank the carriage toward the tailstock end of the bed and carefully slide it off the end of the lathe. Be careful to support the lead screw so as not to bend it.You'll then have access to the whole lead screw and all of the parts of the carriage.The advantage of doing it this way is that you won't alter any of the settings of the parts of the carriage. You can just clean things up and reassemble, or you can move on to attempting to adjust or modify whatever you find.Best of luck and let us know how it goes.ShopShoe
A plastic CD case is/was the material of choice to make that cover.