Definitely get the lathe, and table up the stairs separately. Even if attached to some strong boards, one tilted on the stairs, the combo together will have all the weight on the legs on the lower side. You might even have to add weight on the front end, to keep things from rolling over backwards. Just look at the pic, and rotate it the 45 degrees or so that the stairs are, you can easily visualize how the weight will shift.
I would remove the lathe from the stand, and bolt it to two 4x4's that are 2 feet or so longer on the side that will be on the bottom side when going up the steps. That will also spread out the weight on the individual steps.
I would also consider dragging the table up the steps on its top. Same thing, that will put the weight on the bottom, and also spread out the load on the steps.
If you don't have one, I would also spend the $75 to $100 for a 5000lb winch, and borrow the battery from a car. Everybody present will appreciate it. Maybe even a few dollies for moving the parts on the level surfaces.