No, Derek! ~~ she would not be correctly styled so in that case. She would be Lady Whateverhisnamewas. Even if he was also coincidentally called Carthy, she would, as you yourself point out, be "Lady Carthy" -- tho idiomatically she might be mentioned as "Lady (Eliza) Carthy" in contexts where necessary to differentiate her from some other knight's wife whose name also happened to be Carthy.

I repeat ~~ The only person correctly styled "Lady Forename Surname" is the daughter of a duke, marquess, or earl.

~M~