No help on taking care of the lathe...
Also, I have a standard Harbor Freight engine hoist. Any tips to get the lathe back on its stand?
Yeah... Don't use an engine crane. They're designed for one purpose....
OK, with that out of the way, yeah, they're quite stout and versatile, but unless you've still got wheels holding the car off of the ground, the legs are problematic. Step one is to think it through, and even do "dry runs" to test theories about how far stuff can "really" reach.
One option MAY be to take the bench out of place, so that you can access the headstock end, and come in from that side. Prolly going to be too wide still, but worth the time to know that.
Another option MAY be (and you're gonna hate this), to block the bench up at it's end extremes, such that the hoist legs can fit underneath of it. Then plant the lathe on the bench. Then lower the bench. Then move the whole assembly to it's final destination.
No matter how you do it, and no matter how much math and geometry you know, do the "dry runs" without lifting the lathe. With those crooked legs, you (usually) find places where it should fit but doesn't, and places that it can't possibly fit but actually does. It's kind of sketchy to "practice" with a significant weight hanging high, and quite close to the "leg wheels" which will inherently be swiveled "short" while you're pushing it forward....