To come back to this, I just found a 512x512 ICO file on the internet, which I loaded into a project of mine, and copied and pasted to a GMX project, and both of the projects loaded fine with LGM.
This was the ICO file that worked.https://www.dropbox.com/s/qc58z4kizehqy9h/512icon.ico
So I went to investigate further the program you used to convert the image, and sure enough it outputs corrupted Icon files when a size layer bigger than 192x192 was exported.http://converticon.com/
I went there and attempted to convert the following 512x512 PNG of the Death Star to a 512x512 ICO
Then LGM had an exception trying to use it on a project just like the one you are getting, so my advice to you is to find another image converter.
That image converter did not work on ICO files larger than 192x192.
Exception in thread "AWT-EventQueue-0" java.lang.IllegalArgumentException: Width (0) and height (0) cannot be <= 0
at java.awt.image.DirectColorModel.createCompatibleWritableRaster(Unknown Source)
The reason is because every layer above 192x192 had a size of 0, which most likely means this image converter can't export ICO's at sizes larger than that, I went through and looked at the size of every layer, up to 192^2 was fine.
Something is clearly wrong with that converter, so please, use a different one.