Later versions of my Asian lathe had volute spring type covers over the leadscrew. Unfortunately, these look to require a lot of stripping to fit, so have refrained from retrofitting to mine.
From time to time, I move the saddle to the Tailstock end of the bed, and engage the drive to the leadscrew, and then hold an old tooth brush against the leadscrew. Ceertainly do this before any screwcutting, to minimise risk of carrying rubbish into the halfnuts. If the direction of rotation of the screw has been chosen correctly, the rubbish, (swarf/dust/grease) gets worked up to the headstock end and out of the thread.
Old toothbrushes are useful for this sort of work, as well as cleaning taps, dies or drills after use. They are cheap, and disposable, although mine usually will have been cleaned a few times in white spirit before being discarded finally.
Not tight, just careful y'ken!
Howard