You have “Cut Selected Graphics and Use Selection Origin” enabled. But it l looks like you only have the outline selected, which is a tool layer. Select all (Ctrl + A) and try again.
There is no way to do a line operation on an image. You will need to convert that image to a vector to use line mode. You could do an image trace, but Lightburn doesn’t have the ability to do a center line trace, so you will end up with double lines. For a simple cutout like this, just redraw it in Lightburn.