Not quite so. Lead screws can be very accurate. Not sure what are the numbers you measured. It is common to speak of a ball screw in terms of accuracy over a given length. Thus, for instance, a C5 accuracy grade would mean about 0.03mm acceptable error in travel over 300mm. Accuracy grade definition varies from one manufacturer to another, so the above example is not dictated by a standard.
Lead screws can easily hold those accuracies. So, when using ball screws it's not really an accuracy demand. Ball screws allow you to have minimal backlash (practical zero), which is often desired in a CNC application. Also, ball screws run quieter and higher speeds can be achieved without the risk of heating the nut and wearing it. Of course they wear slower. Theoretically you can have a lead screw set up to have zero backlash, but it will hardly last.
Forgot your lathe was Chinese, so the original screws may have been poor quality and not as accurate