LightBurn will not find, directly connect with, or have “live control” of that motion controller, but can produce gcode files that you can indirectly open and execute from within the UCCNC software, although TBH the laser results I’ve seen so far are underwhelming (example), but you may have better success.
On the other hand, if you are looking to do router work, then MillMage should produce gcode files that will run fine on your machine and there is a UCCNC Custom GCode ‘Flavour’ available to select when setting up the device:
