Preeeeety sure it's not Livia... I mean, we pretty clearly killed her in the Praetorium, and if that's not enough Cid asks Lucia whether or not she was out for revenge against us for killing her sister.
Fakeout deaths have happened before (or: Nanamo visibly asphyxiating and then turning out to be fine cuz "it was just a sleeping potion lolz"), so I'm not ruling it out, but.
As for where Livia got her skills, up in the air but it's probably not the same place Yda did. Pureblood Garlean war orphan vs. (implicit) Ala Mhigan refugee turned Sharlayan scholar, their backgrounds are very different.