"Lady Eliza Carthy" could only be her title if she were the daughter of a duke, marquess, or earl; which she is not. To get a title, she would have to have her MBE raided to a DBE, when she would become "Dame Eliza Carthy". Or else get a life peerage, which would make her "Lady Carthy" or "Baroness Carthy" (of Somewhere-or-Other). Might happen eventually; she is quite young, after all.

~M~