Making a lead screw is an interesting subject. The techniques used depend a lot on the precision that is needed in it. If all you need is one for average shop use, then you could just purchase some threaded rod and cut or add to the ends as needed for the particular lathe. That is probably the easiest way.
From that point, things can get more difficult. Some have mentioned just cutting it in two or more sections, synchronizing the threads as you go. That can add discontinuities at those points where the threads have to be matched.
A thread chasing head (a big die) can cut a thread of any length, but any error in the pitch of the die will be reflected along the entire length of the screw produced that way.
Another consideration is if you intend to cut the screw on the lathe that has a worn screw, then things get real dicey. Most lead screws will have a lot of wear in the area near the headstock and the remainder will be almost factory perfect. This wear will show up as changes in the pitch of the thread that it cuts. As you cut away from the headstock the pitch (in TPI) will first increase, then go back to the nominal value, then decrease, and finally go back to that nominal value. And, due to the differing lengths of the many threads that have been cut with it, these errors may not be symmetrical. The increase in TPI may happen over a smaller distance than the subsequent decrease.
Many techniques have been used to decrease the errors when cutting lead screws. One such technique is to make two screws and mount them in opposite directions on a lathe that has provision for turning both of them at the same time. The cutting tool is guided from a point that is on a bracket that is connected to nuts on both of them and is half way between the points where those two nuts are attached. This will average out some errors. BUT NOT ALL OF THEM. Another technique is to make the nut(s) relatively long so that they will average out any local errors in the original screw(s) that are used.
Master screws are lapped with a long lap that spans many threads, again to average out any errors that may exist in the original cutting. These lapped screws are not for use on a production lathe, rather they are used, along with other techniques, to make the final product.
Of course, with any of this you need to be able to measure and verify the accuracy as you are cutting them. Break out the Jo blocks.
I suspect that my first suggestion, just purchasing some threaded rod, may be the best choice in your case. Frankly, it is probably what I would do.
