Roy,
a lathe works either on Diameter or radius, I prefer diameter. So in essence when the tool is on centre that is zero dia (or radius) and moving away from centre increases the dia thus the axis is moving positive.
Z is the similar to a Z on a mill, if you think of a mill with the surface of the material being zero then everything you mill off will be a negative value. In a lathe it is normal to set the end of the stock as zero then as with the mill everything cut off will be a negative value.
Now some people like to set things differently (especially router guys
) and really its up to them but the above is standard practice and fairly easy to get your head around and can avoid confusion if ever needing to ask questions.
Hood