If it runs Mach3 today then no, it’s almost certainly not compatible with LightBurn. You may be able to generate gcode that could be run in Mach3 but no certainty in that and you’d likely need to modify the gcode in some way.
I assume you’re referring to a motion control board. If so, then no, LightBurn does not directly control hardware devices. It communicates with specific controllers to accomplish the task of running a laser.
The LightBurn website lists the type of controllers supported: LightBurn Software