I have zero experience with this particular software. When you send a job, is it done as a ‘print’? The laser would appear as a printer in this case. LightBurn does not support direct comms with printer driver lasers, but can send files in a roundabout way:
Otherwise, you may have to stick with that software, or swap the machine’s controller out for a modern replacement that is compatible with LightBurn. It looks like a sturdy machine, but as with any machine tool, you can have the best looking hardware in the world but if the software is difficult, the machine will be too.