The convention with CNC is that the Z reading, the longitudinal axis, decreases towards the headstock; while the X axis, the cross slide, decreases towards the spindle centreline. Normally one sets the tool so that the actual cutting diameter is indicated on the DRO.
If you have aDRO that can accomodate tool offsets, then this is a logical way to work: you reference the lathe with some reference tool, or other way of "homing", so that when you dial the tool number into the DRO it will indicate the actual diameter that tool will cut.
One way to handle Z is then to zero the Z axis on the very end of the bar sticking out from the chuck, and then all your measurements on the part are negative.
You don't have to do it this way but it is a sort of standard.