M3 Nano Lightburn Supported?

No. M3 Nano or any of the Nano family will not work with LightBurn, at least not directly.
Meerk40t is an open source laser control software that works with M2 Nano and other boards common in K40 systems. It’s possible that they’ve added supported for M3. Meerk40t also does some interesting things in terms of emulating Ruida and GRBL controllers. Some people have used that to use LightBurn through Meerk40t to control their otherwise unsupported lasers. Note that I have not seen any real investigation into how well this is working for people who do use it. I get the impression that this functionality is somewhat experimental.