That's just like torch height control on a plasma.
You would want it to do more than just one axis though..... you may be able to reach out to a motion control company to get more help. 
Vital Systems' HiCON Integra has torch height control, they may be able to help you with this or point you in a direction you can start with.

I literally just came across this idea on linuxcnc with using external offsets to control torch height. Based on your feedback, I may start the implementation with one axis then but I haven't heard of Vital Systems' HiCON before you so I need to reach out to them. If you have any more ideas, I would be super gracious! I might have underestimated the complexity of this project so I may attempt easier implementations until I get a stronger understanding.

https://www.vitalsystem.com/index.php

There are a few motion controller suppliers for Mach4.  Having only ever used two of them personally (my dad used more with Mach3); I really like the HiCON from vital systems. 
The guys there are very helpful as well.