Ok well the ballscrew itself is really just the shaft, the ball nut is the part that goes along the screw, the ends are up to you. You can get blocks with bearings already in or you can use the brackets you already have on the lathe and fit bearings to them.
Normally the nut is held rigid and the screw rotates. As the screw rotates then you need to have bearings, sometimes just one end as is usual on the X axis, sometimes both ends as is usual on the Z, BTW X and Z here are referring to a lathe.
Ok so bearings are needed but in addition the screw can not be allowed to move axially as if it does then you get backlash. The way this is solved normally is to use a pair of precision angular contact bearings at one end, the other end can just use a normal bearing.
The blocks on the link I attached will have these bearings in them, how good a quality I have no idea.
Hood