Your move has multiple stages. First you have to get it off the floor safely. Second you need to move it to the loading area. If it can be moved on a continuous surface to outdoors, all the better.then. Only then, you need to get it on the trailer.
If this is in an industrial area, check adjoining businesses to see if they have a forklift and, for a consideration help you load it.
You least risky way is to hire a rigger. For a lathe that nice, I'd seriously consider it, unless the fees for that area are prohibitive.
If you are going DIY, you will need a toe jack to lift the lathe, and 4"X4" wooden wedges to sustain your progress. (mine are 24" long) You lift in appropriate increments - about 1/2 of an inch - until you can set it on machine skates. Machine skeates are well worth the investment.
****warning*** lathes topple very easily, even the Monarch 10ee . You never use 4 skates to move a lathe. (there are too many horror stories). You use a single skate at the tailstock end, and two skates on the headstock end. There is an exception for Ton Lipton style skates, where you end up with 4 rolling elements, be they are tied together in pairs.
There are several ways to do the final lift. by far the easiest is to use a drop deck trailer (from Sunbelt rentals). These are a game changer, especially for a first-timer.