if the belt is connected with an "alligator" splice, you can find a way to pull the center (plastic, rawhide,etc material) pin. Then it is easy to reconnect.
If you are moving the lathe to set up for yourself somewhere else, you probably won't want to damage the belt, then have to buy a new one or re-splice it.
If moving to sell, you will get more for an assembled lathe in running order, than for a pile of assemblies needing to be re-connected with some missing or damaged parts such as the belt.
If the belt is endless, in a pinch, you can loosen some set screws and pull the shaft on the backstand idler. Don't mess with the spindle.
I would find 2 moderately strong friends. Unbolt the lathe and idler from the bench, and take the motor off. Then have 2 of you carry the lathe, while the 3rd tags along with the backstand idler.
smt