You can find a color map here:
Vector shapes imported to LightBurn will respect the color layers or do a closest match fit. Keep in mind that LightBurn only supports 29 cut layers in a single project.
Having said that, if your current SVG is importing as black, even if the original image is in color, this makes me think the contents of the SVG is actually a raster image rather than a vector image. In that case no real mapping is possible. You could attempt to trace the image in Inkscape and then import but you’re likely needing to do a whole lot of editing to make that useful if the original is meant to hold cut layers.
However,