I don’t play with Illustrator that often, but as I understand, the Adobe Illustrator Mask (along with other graphic editing tool) is a nondestructive action, so all the art is technically still there. This can cause issues when importing into LightBurn, no matter the file format. In AI, ‘Bake’ (or it might be called clip?) the masking into your project prior to export, that should retain the desired resulting image as designed. 
Please update us with how you progress.