First off, I’m sorry for mentioning GRBL since this is C3D and it could have GRBL-LPC or it could have Smoothieware on it and there was no mention of what firmware is on the C3D board or even how you got it.
If you obtained the C3D from Cohesion it most likely has Smoothieware already installed and it came with a uSD card which has a file named config.txt.
Where did you get the C3D board that is in the machine?
Who installed the C3D into the machine and what instructions did they follow for installation?
I would’t expect LightBurn to show you OMTech as a choice because LightBurn communicates with the machine’s firmware so that is generally what you’d be looking for. But I see from that link the machine is not likely to come with the C3D.
Since you said you are running Windows, there are drivers for Windows USB system which I believe need to be installed. Did you install the C3D using these instructions and also follow the link on the bottom of this page for installing drivers for Windows? https://cohesion3d.com/knowledgebase/k40-with-m2nano-cohesion3d-laserboard-installation/
As far as what direction to take goes, we are still working on figuring out what you have, how it might be setup.