Hi David

The play could be in the leadscrew if it's worn (or made that way), but it could also be in the thrust bearings, ie the bearing arrangement where the handwheel is.

These are usually adjustable, or sometimes a bearing that can be changed. Suggest you have a look under the cross slide and see where most of the play is.

If its the leadscrew, it's probably the nut that's worn, which could be made on the lathe (out of phosphor bronze), which would be a nice project to get to grips with internal screw cutting.

Will

There are also 2 more adjustments you could look at
1. Under the crosslide there should be a locking nut check this out for either slackness or even being
loose.
2. Jib strip adjustment grab hold of the variose parts of the cross slide be quite brutal and push backwards an forwards to check if any movement. if so adjust the grub screws
I hope thit is of some small help

Bob