Whomever is doing the 'rigging" is using a light duty strap binder as the 'red sling'. Those strap binders are used for securing loads like motorcycles, barbecue grills or canoes to trailers or pickup beds. Those strap binders are unsafe to use as lifting slings.
The sling made up around the spindle of the lathe looks to have been wrapped a few times to take up for long length. Plenty of slack still in it. When the forklift comes up to take the load, there is going to be a lot of slack to be taken up in that sling on the spindle. No telling how the lathe will hang off the forklift.
Whether the lathe is light weight or not, rigging off the spindle is not something I'd recommend. Many lathe manufacturers will give rigging instructions based on the center of gravity of the lathe being somewhere towards the headstock end of the bed. They will sometimes call for putting slings around 'girths' or cross-members cast into the bed. Other manufacturers will call for slinging around the lathe bed, but also call for wood blocking to hold the slings off and clear of the lead screw and feed rod.
I suppose the person doing the 'rigging' in this photo could have done worse: wrapped a chain around the bed, unprotected, and tied a knot in the chain to connect the two ends of it.
I am reminded of an incident a bro of mine related to me, concerning the use of those strap binders as lifting slings. A friend of his who had spent his career in the heavy construction trades and had done a good bit of rigging wound up with a bad compound fracture of his leg. The fracture resulted from this friend taking a shortcut in doing some rigging in his home shop/garage. The friend was working on a light trailer frame and had to pick it up and stand it on edge for some work he needed to do to it. He had a gantry in the shop with a chainfall, and had some proper slings. Instead of getting the slings, this guy took a strap binder that was at hand, and used it as a sling. He told my bro that as he made up the rigging with that strap binder, his 'inner voice' was telling him 'don't do it... it's unsafe.... use a sling'. His other inner voice was saying: "It's only a light trailer frame...." As this guy raised the trailer frame and it started to stand on edge, using the strap binder as a sling, the strap binder let go. The frame came down, caught the guy in the leg, laid him out on his shop floor and busted his tibia with a compound fracture. Surgery, pinning of the fracture and a slow recovery were the outcome.
We had a saying at the powerplant where I retired from: "Most accidents happen at home." At work, with the right equipment and enforced safe work practices, there was a lot less likelihood of taking a shortcut and having an accident. The guy 'rigging' the lathe in this photo will be unlikely to drop the lathe or have it get away from him, but how it hangs on his 'rigging' and whether damage to the lathe results is another matter.