LocalThickness_ expects a binary image. Thus after Invert call Process > Binary > Make binary. Binarization also makes the image 8-bit, so you can drop that step from your workflow. The plugin ran successfully on my computer after binarization, but took a little while despite my workstation being quite powerful. The same method will work with the stand-alone plugin. I need to add more documentation to the wiki page of
LocalThickness_, thank you for pointing out this omission.
LocalThickness_ doesn't actually expect a binary image, it works with any 8-bit grey-scale. Processing a grey-scale image takes a lot longer than binary (10+ minutes), and the results make more sense in the latter case at least to my untrained eye. Also at the moment the plugin accepts an 8-bit colour image, which it shouldn't. I'm afraid this bug is my handiwork.