Use different colors for layers in Corel, not actual layers. LightBurn will import the colors in Coreldraw to the closest matching color layer in LightBurn.
Which version of LightBurn are you running? I don’t have this problem, though it’s possible that you’ve got anti-virus or firewall software preventing the Corel macro helper tool from communicating with LightBurn. There’s a utility called ‘SendUDP’ that checks to see if LightBurn is running, and if it is, will send it a command to load the file that was exported from Corel instead of launching a new copy of LightBurn. If that tool was prevented from sending the command, that would cause the issue you’re seeing.