That would work if your lathe is a metric lathe instead of Imperial. Best to check. The thread on the leadscrew is typically a British Standard Whitworth (BSW), left hand. Measure the TPI and you might be able to find a tap to make your own nut. You can also buy internal threading bars in the BSW pattern and screw cut it.
Another option is to buy some Acme LH threaded stock and make an Acme LH nut. The Emco BSW arrangement is smoother in use (yes, I tried this) and I would go with an Acme as a last resort.
I cannot recall what the nut looks like but the typical larger Emco lathes have two screws on the cross slide; one to attach the nut and one for a set screw that adjusts backlash on the nut. The nut has a slot at the rear and the screw, which has a coned tip, pushes on the end of the nut and collapses the material via that slot. It allows for zero backlash on an Emco lathe, something they are known for.
The crossfeed screw measures .3082 OD, it could be either 5/16 (.3125) or 8mm (.3149) Pitch gages either 1.25 or 20 TPI (1.25 = 20.32 TPI so it's hard to tell). BSW 5/16 is 18 TPI, 5/16 NC is 18 TPI, 5/16 NF is 24 TPI. So it appears that the screw is 8mm x 1.25 LH by process of elimination.
The nut was split and has a backlash adjustment screw. It would have worked better on a brass or steel nut, the zinc alloy crumbled away. Zero backlash is nice but since I never trust it anyway it isn't particularly useful.
My Super 11 is an Imperial machine and had Imperial screws on the cross slide and compound. The longitudinal feed is Metric. My cross slide is a LH 1/2-10 BSW threaded screw with a Zamack nut. If yours is Imperial then I would guess the lead screws are Imperial also, although I cannot find what the TPI is.
The backlash adjustment presumably reduced chatter so it had some value. I always back off and come back in to the next cut setting anyway but it isn't necessary; mine has zero play.
I know this is an old thread but I have been looking for parts for my Emco Compact 8 and figured out it is the same model as the Sears Craftsman 2893. ereplacementparts dot com has a bunch of parts for that model. I tried to post the actual link but the post kept getting rejected? Makes for a less than useful blog site when you can't post links?