Jon,
I never can keep straight which axis is X and which is Y, except that I think I remember that they are not the same on a lathe as on a mill. But if you are calling left-right "X" and IN-OUT "Y", then on a used mill, more backlash would be expected on the X than on the Y. Say you are cutting a longitudinal slot in 100 shafts. In most cases, once you get the IN-OUT set and locked, you won't touch it again until you are finished. So the cross-feed nut will typically have more wear than the IN-OUT one.
There are three possible sources of backlash in either feed system - running clearance between nut and screw, end float in the screw, wear in the nut and wear on the screw. To determine what part or parts need to be replaced, you first need to adjust the screw end float. This is best done with the feed nut disengaged from the feed screw. But you can't do that on the main cross feed because the screw has bearings at both ends and the nut runs between the bearings. You can do this on an Atlas lathe because the cross feed has only one bearing, and when you crank the nut off of the screw, you still have an adequate engagement between the cross slide and the carriage dovetail. I don't happen to know whether you can crank the IN-OUT nut off of its screw or not.
Anyway, first adjust the feed screw end float to .001"-.002". Or to as low as you can get it without there being any significant drag on the crank when you rock it back and forth. Then measure the backlash out in the middle of the slide's travel and right near the end of the travel. If there is a significant difference between the two measurements, the feed screw is worn. Any backlash in excess of 0.005" to 0.010" near the stops is feed nut wear. Anything over about 15 thou near the stops would indicate that you should replace the feed nut.