If the problem also occurs in Jarvis mode, then it does not have anything to do with an image engraved in Grayscale mode.
If the problem were due to “losing steps”, then the images would become more displaced during the engraving. That does not happen in any of your examples.
Its nor related to the “greyscale image mode”, it happens with all modes…
Its any grayscale image that leads to the problem, all pure black engravings are accurate…
Maybe try this: add a two-pixel solid black border around the image in an image editing tool (not using LightBurn). Then import it again and check what happens. Would be interesting