Next time you need to move one, You can use 2 of these 36 inch straps, You thread them behind the leadscrews and then bring them around the lathe bed to meet at the top. Then hook all 4 eyes together with a shackle, then use a short chain to connect to the hook on your cherry picker.
Once you start lifting it, You have 2 built in leveling devices, No need to buy one. You roll the carriage in the direction you need to go to balance the load, And secondly you can move the tailstock along the bed also to level the load.
Usually a couple inches to maybe 10 inches in front of the chuck is where you are going to place the straps to get things perfectly level and have enough travel with the carriage to get it level.
You can lift the lathe just off the floor barely enough to let it move and pull it into the place you are wanting to go with the cherry picker.
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