The controller you have is a Trocen AWC 708. It has no ability to set rotary options from software - you have to do it from a menu on the controller itself. This isn’t a “LightBurn doesn’t support this yet” any more than my “Honda Civic doesn’t have a ‘Launch into orbit’ option yet”. 
On the controller, press the Menu button. Then go to 7) Common Parameters Setting, then 4) Rotate Engraving and Cutting. From here you can enable the rotary, set the steps per rotation, and diameter. This is the only place you will ever be able to do this until such time as Trocen updates their firmware to allow software to make the changes.
The nice thing is, the settings here only affect the rotary, and if you just turn off the ‘Rotary Enable’ setting here, nothing else is affected and it all goes back to normal, so there’s little chance of messing up something else.