...paperwork is the bane of her existence, obviously xD

But more realistically speaking, Livia isn't some all powerful person. While she is very powerful, she had no idea what was the strength of the so-called 'god', the Phoenix, and she doesn't believe herself to be powerful enough to confront a god yet.  So, she basically sent someone there to gauge just how strong it was....basically she sent them there to possibly die.

Keep in mind Livia is more of a manipulator, and not entirely a saint. She doesn't like doing things she can send someone else to do if its something she deems not worth her time. If they died, then she knew it was as powerful as the legends say, and the next time after some preparation, she'd confront it herself.

If she lost an ally in the process of that, then well, that's just how it is.

As for Katherine, she'd send her because as her pupil and former student, Katherine is strong, but not as strong as Livia is (probably). So if Katherine can handle it, and if that's as powerful as a 'god' actually is, then she sure as hell is strong enough to fight one.

So basically Livia wouldn't go herself because she Needed to safely see how strong the Phoenix is.