When I press Reference All Axes, the Z axis on my lathe homes in the positive direction.  I need it to home in the negative direction.
I changed the direction in Control, but regardless of what direction I choose, the Z axis homes in the + direction.  I have restarted Mach4, restarted the PC, changed direction to + and - but no matter what I do, the lathe homes in the wrong direction.  Jogging works in the correct direction, BTW.

See attached document for screenshots of the configuration.

Configure > Control > Homing > Here you select the direction.
If that's not fixing it, something's broken send an email to support.

Not sure your entire system setup.  However I have had this issue in the past.  It happened when one of the wires for the directional input to the stepper driver broke.  If that happens no matter what you do your motion will only be in 1 direction.