Here is a small historical collection of responses from Oz on this subject.
LightBurn:
As far as I know, Trocen controllers do not have the ability to alter the Z axis during a cut. I have found nothing in LaserCAD that will do this, so I have sent a message to Trocen to ask if this is even possible, and if so, if they will share the commands with me to do so.
Followed by:
Trocen has responded - there is no way to do this with their hardware.
Dec '19
LightBurn:Trocen gives me almost no control of the Z in software, so you won’t have the option to enable the Z. The jog buttons normally work even if you don’t have Z enabled, but with the Trocen controller they’re disabled because I have only found a way to move the Z with continuous moves, not discrete steps.
Nov '20
LightBurn:Trocen controllers do not have the ability to move the Z axis within a running job like some other controllers do, which is why you don’t have those options.
Each laser system supported by LightBurn has its own set of features and limitations. Trocen / AWC controllers provide their unique access and control from software which differs from other motion control systems LightBurn supports. As you review posts, read our documentation, watch videos or consume other resources showing LightBurn, you may see reference to a feature that may or may not be available to you and the control system of your laser.
Here is another example: