Can someone speak loshon hara to themselves about someone? Or is another person required?
There is no prohibition of lashon hara about oneself.
Nonetheless, it is not recommended to denigrate oneself – for many reasons.
Shut Le-Chafetz Chaim (Rosner, no. 24); see also Chafetz Chaim 7:6.
It also stands to reason that there is no prohibition of lashon hara about oneself; the crux of the prohibition of lashon hara is a flaw in middos, and this flaw does not apply to somebody speaking about himself.