The easiest way to solve this problem will be to Force Reinstall LabVIEW. However, since this is a time consuming process, you can also try several other solutions.
Make sure that the following folders have read-write access:
...\My Documents\LabVIEW Data\Icon Templates\
...\My Documents\LabVIEW Data\Glyphs\
You may also want to run LabVIEW as an administrator, to mitigate other file permission errors.
The Icon Editor is a VI Template, which can be found at ...\<LabVIEW-Version>\Resource\Plugins\lv_icon.vit. You can take a look to make sure this is still located in the correct place and does not have any errors.