Would an older Liz technically be a Camilla Alter?
Something I've considered myself. In this instance, I'd say no. Rather, it'd be a situation similar to Saber Altria and Lancer Altria (Same person but different paths through life that lead to different outcomes.)
That said, you could 'technically' call Elizabeth, as she is, Carmilla Lily. Being that she is Carmilla at the start of her legend. (Much like Altria Lily being the Altria who just pulled Caliburn, and Medea Lily being the somewhat naive princess who hasn't been betrayed yet)