As an invisible spy, your hat is supposed to be invisible, but the Cheater's Lament is not. This means other people can see the hat floating around and kill you when you're supposed to be undetectable. This is unfair, as it gives the spy a gameplay disadvantage for using this hat. I think it should go invisible like all the other hats. (I have tested this several times, including scaring myself while invisible on Harvest Event, and I still see that the Cheater's Lament is completely opaque.)
NOTE:
This is a copy of a bug report I submitted to Valve, but I'm also posting in here just in case it has something to do with CrossOver, which I kinda doubt.