...also... lathes must be the biggest pain in the butt to get a sling around. All the weight is at one end, it's top-heavy, full of smooth surfaces and festooned with bendable lead screws and handles!
Which is why all good machine movers/carriers have plenty of short lengths of 3x2, 3x3, and 4x2 timber to act as packings to keep lifting slings away from shafts and screws, backed up with plenty of rubber packings to protect slideways.
The handiest pieces of kit on my hiab truck are a pair of 6' lengths of 1.5 and 3 ton chain, plain at one end and a clutch shortener at the other. They're incredibly versatile when it comes to needing an adjustable sling or a balance chain. Both tested and certified, I wouldn't be without them. I also carry a 2 ton lever hoist for telecoms work, but the clutch chains are invaluable. I used to have 4 lengths of 4x4x3/8 angle for putting between lashing chains and square ways, and I can vividly remember machining the radius out on a crank shaper so they'd butt up to a square corner.